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<h1 style="display: none">LaTeX数学笔记</h1>
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本文最后更新于：November 11, 2022 am
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<h1 id="latex-数学笔记"><a class="markdownIt-Anchor" href="#latex-数学笔记"></a> <em>LaTeX</em> 数学笔记</h1>
<h2 id="希腊字母"><a class="markdownIt-Anchor" href="#希腊字母"></a> 希腊字母</h2>
<table>
<thead>
<tr>
<th style="text-align:center">语法</th>
<th style="text-align:center">大写</th>
<th style="text-align:center">小写</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">大写</th>
<th style="text-align:center">小写</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">alpha</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">A</mi></mrow><annotation encoding="application/x-tex">\Alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">A</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.0037em;">α</span></span></span></span></td>
<td style="text-align:center">beta</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">B</mi></mrow><annotation encoding="application/x-tex">\Beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">B</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05278em;">β</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">gamma</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Γ</mi></mrow><annotation encoding="application/x-tex">\Gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Γ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05556em;">γ</span></span></span></span></td>
<td style="text-align:center">delta</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Δ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>δ</mi></mrow><annotation encoding="application/x-tex">\delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03785em;">δ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">epsilon</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">E</mi></mrow><annotation encoding="application/x-tex">\Epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">E</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">ϵ</span></span></span></span></td>
<td style="text-align:center">zeta</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Z</mi></mrow><annotation encoding="application/x-tex">\Zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">Z</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ζ</mi></mrow><annotation encoding="application/x-tex">\zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.07378em;">ζ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">eta</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">H</mi></mrow><annotation encoding="application/x-tex">\Eta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">H</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>η</mi></mrow><annotation encoding="application/x-tex">\eta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">η</span></span></span></span></td>
<td style="text-align:center">theta</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Θ</mi></mrow><annotation encoding="application/x-tex">\Theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Θ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>θ</mi></mrow><annotation encoding="application/x-tex">\theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">θ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">iota</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">I</mi></mrow><annotation encoding="application/x-tex">\Iota</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">I</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ι</mi></mrow><annotation encoding="application/x-tex">\iota</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">ι</span></span></span></span></td>
<td style="text-align:center">kappa</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">K</mi></mrow><annotation encoding="application/x-tex">\Kappa</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">K</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>κ</mi></mrow><annotation encoding="application/x-tex">\kappa</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">κ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">lambda</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Λ</mi></mrow><annotation encoding="application/x-tex">\Lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Λ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">λ</span></span></span></span></td>
<td style="text-align:center">mu</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">M</mi></mrow><annotation encoding="application/x-tex">\Mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">M</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>μ</mi></mrow><annotation encoding="application/x-tex">\mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">μ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">nu</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">N</mi></mrow><annotation encoding="application/x-tex">\Nu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">N</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ν</mi></mrow><annotation encoding="application/x-tex">\nu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.06366em;">ν</span></span></span></span></td>
<td style="text-align:center">xi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Ξ</mi></mrow><annotation encoding="application/x-tex">\Xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Ξ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.04601em;">ξ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">omicron</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">O</mi></mrow><annotation encoding="application/x-tex">\Omicron</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">O</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ο</mi></mrow><annotation encoding="application/x-tex">\omicron</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">ο</span></span></span></span></td>
<td style="text-align:center">pi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Π</mi></mrow><annotation encoding="application/x-tex">\Pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Π</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">π</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">rho</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">P</mi></mrow><annotation encoding="application/x-tex">\Rho</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">P</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ρ</mi></mrow><annotation encoding="application/x-tex">\rho</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">ρ</span></span></span></span></td>
<td style="text-align:center">sigma</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Σ</mi></mrow><annotation encoding="application/x-tex">\Sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Σ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">σ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">tau</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">T</mi></mrow><annotation encoding="application/x-tex">\Tau</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">T</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>τ</mi></mrow><annotation encoding="application/x-tex">\tau</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.1132em;">τ</span></span></span></span></td>
<td style="text-align:center">upsilon</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Υ</mi></mrow><annotation encoding="application/x-tex">\Upsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Υ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>υ</mi></mrow><annotation encoding="application/x-tex">\upsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">υ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">phi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Φ</mi></mrow><annotation encoding="application/x-tex">\Phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Φ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">ϕ</span></span></span></span></td>
<td style="text-align:center">chi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">X</mi></mrow><annotation encoding="application/x-tex">\Chi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">X</span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>χ</mi></mrow><annotation encoding="application/x-tex">\chi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">χ</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">psi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Ψ</mi></mrow><annotation encoding="application/x-tex">\Psi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Ψ</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ψ</mi></mrow><annotation encoding="application/x-tex">\psi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">ψ</span></span></span></span></td>
<td style="text-align:center">omega</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Ω</span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">ω</span></span></span></span></td>
</tr>
</tbody>
</table>
<h2 id="二元算符"><a class="markdownIt-Anchor" href="#二元算符"></a> 二元算符</h2>
<table>
<thead>
<tr>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">\times</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">×</span></span></span></span></td>
<td style="text-align:center">\div</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>÷</mo></mrow><annotation encoding="application/x-tex">\div</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">÷</span></span></span></span></td>
<td style="text-align:center">\cap</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∩</mo></mrow><annotation encoding="application/x-tex">\cap</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.55556em;vertical-align:0em;"></span><span class="mord">∩</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\pm</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">±</span></span></span></span></td>
<td style="text-align:center">\mp</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∓</mo></mrow><annotation encoding="application/x-tex">\mp</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">∓</span></span></span></span></td>
<td style="text-align:center">\cup</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∪</mo></mrow><annotation encoding="application/x-tex">\cup</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.55556em;vertical-align:0em;"></span><span class="mord">∪</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\cdot</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⋅</mo></mrow><annotation encoding="application/x-tex">\cdot</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.44445em;vertical-align:0em;"></span><span class="mord">⋅</span></span></span></span></td>
<td style="text-align:center">\ast</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∗</mo></mrow><annotation encoding="application/x-tex">\ast</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46528em;vertical-align:0em;"></span><span class="mord">∗</span></span></span></span></td>
<td style="text-align:center">\odot</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊙</mo></mrow><annotation encoding="application/x-tex">\odot</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">⊙</span></span></span></span></td>
</tr>
</tbody>
</table>
<h2 id="关系符号"><a class="markdownIt-Anchor" href="#关系符号"></a> 关系符号</h2>
<table>
<thead>
<tr>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">\equiv</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≡</mo></mrow><annotation encoding="application/x-tex">\equiv</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46375em;vertical-align:0em;"></span><span class="mrel">≡</span></span></span></span></td>
<td style="text-align:center">\cong</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≅</mo></mrow><annotation encoding="application/x-tex">\cong</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.589em;vertical-align:0em;"></span><span class="mrel">≅</span></span></span></span></td>
<td style="text-align:center">\leq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">≤</span></span></span></span></td>
<td style="text-align:center">\geq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≥</mo></mrow><annotation encoding="application/x-tex">\geq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">≥</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\neq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">≠</mi></mrow><annotation encoding="application/x-tex">\neq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mrel"><span class="mrel"><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="rlap"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="inner"><span class="mrel"></span></span><span class="fix"></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span><span class="mrel">=</span></span></span></span></span></td>
<td style="text-align:center">\simeq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≃</mo></mrow><annotation encoding="application/x-tex">\simeq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46375em;vertical-align:0em;"></span><span class="mrel">≃</span></span></span></span></td>
<td style="text-align:center">\leqq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≦</mo></mrow><annotation encoding="application/x-tex">\leqq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.01166em;vertical-align:-0.25583em;"></span><span class="mrel amsrm">≦</span></span></span></span></td>
<td style="text-align:center">\geqq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≧</mo></mrow><annotation encoding="application/x-tex">\geqq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.01166em;vertical-align:-0.25583em;"></span><span class="mrel amsrm">≧</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\ll</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≪</mo></mrow><annotation encoding="application/x-tex">\ll</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">≪</span></span></span></span></td>
<td style="text-align:center">\approx</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.48312em;vertical-align:0em;"></span><span class="mrel">≈</span></span></span></span></td>
<td style="text-align:center">\leqslant</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⩽</mo></mrow><annotation encoding="application/x-tex">\leqslant</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7733399999999999em;vertical-align:-0.13667em;"></span><span class="mrel amsrm">⩽</span></span></span></span></td>
<td style="text-align:center">\geqslant</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⩾</mo></mrow><annotation encoding="application/x-tex">\geqslant</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7733399999999999em;vertical-align:-0.13667em;"></span><span class="mrel amsrm">⩾</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\gg</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≫</mo></mrow><annotation encoding="application/x-tex">\gg</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">≫</span></span></span></span></td>
<td style="text-align:center">\sim</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∼</mo></mrow><annotation encoding="application/x-tex">\sim</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">∼</span></span></span></span></td>
<td style="text-align:center">\thicksim</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∼</mo></mrow><annotation encoding="application/x-tex">\thicksim</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel amsrm">∼</span></span></span></span></td>
<td style="text-align:center">\backsim</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∽</mo></mrow><annotation encoding="application/x-tex">\backsim</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.37788em;vertical-align:0em;"></span><span class="mrel amsrm">∽</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\subset</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊂</mo></mrow><annotation encoding="application/x-tex">\subset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">⊂</span></span></span></span></td>
<td style="text-align:center">\subsetq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊆</mo></mrow><annotation encoding="application/x-tex">\subseteq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">⊆</span></span></span></span></td>
<td style="text-align:center">\supset</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊃</mo></mrow><annotation encoding="application/x-tex">\supset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">⊃</span></span></span></span></td>
<td style="text-align:center">\supseteq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊆</mo></mrow><annotation encoding="application/x-tex">\subseteq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">⊆</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\because</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∵</mo></mrow><annotation encoding="application/x-tex">\because</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69224em;vertical-align:0em;"></span><span class="mrel amsrm">∵</span></span></span></span></td>
<td style="text-align:center">\therefore</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∴</mo></mrow><annotation encoding="application/x-tex">\therefore</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69224em;vertical-align:0em;"></span><span class="mrel amsrm">∴</span></span></span></span></td>
<td style="text-align:center">\nsupseteq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊉</mo></mrow><annotation encoding="application/x-tex">\nsupseteq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.09657em;vertical-align:-0.30274em;"></span><span class="mrel amsrm">⊉</span></span></span></span></td>
<td style="text-align:center">\supsetneq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊋</mo></mrow><annotation encoding="application/x-tex">\supsetneq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel amsrm">⊋</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\leftarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>←</mo></mrow><annotation encoding="application/x-tex">\leftarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">←</span></span></span></span></td>
<td style="text-align:center">\uparrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>↑</mo></mrow><annotation encoding="application/x-tex">\uparrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mrel">↑</span></span></span></span></td>
<td style="text-align:center">\updownarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>↕</mo></mrow><annotation encoding="application/x-tex">\updownarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mrel">↕</span></span></span></span></td>
<td style="text-align:center">\Longrightarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⟹</mo></mrow><annotation encoding="application/x-tex">\Longrightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.549em;vertical-align:-0.024em;"></span><span class="mrel">⟹</span></span></span></span></td>
</tr>
</tbody>
</table>
<h2 id="常用数学符号"><a class="markdownIt-Anchor" href="#常用数学符号"></a> 常用数学符号</h2>
<table>
<thead>
<tr>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">\sum</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∑</mo></mrow><annotation encoding="application/x-tex">\sum</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.00001em;vertical-align:-0.25001em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span></span></span></span></td>
<td style="text-align:center">\int</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∫</mo></mrow><annotation encoding="application/x-tex">\int</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.11112em;vertical-align:-0.30612em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∫</span></span></span></span></td>
<td style="text-align:center">\dagger</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>†</mo></mrow><annotation encoding="application/x-tex">\dagger</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord">†</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\prod</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∏</mo></mrow><annotation encoding="application/x-tex">\prod</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.00001em;vertical-align:-0.25001em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∏</span></span></span></span></td>
<td style="text-align:center">\oint</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∮</mo></mrow><annotation encoding="application/x-tex">\oint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.11112em;vertical-align:-0.30612em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∮</span></span></span></span></td>
<td style="text-align:center">\infty</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord">∞</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\partial</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∂</mi></mrow><annotation encoding="application/x-tex">\partial</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord" style="margin-right:0.05556em;">∂</span></span></span></span></td>
<td style="text-align:center">\iiint</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∭</mo></mrow><annotation encoding="application/x-tex">\iiint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.111em;vertical-align:-0.306em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0004999999999999727em;">∭</span></span></span></span></td>
<td style="text-align:center">\forall</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∀</mi></mrow><annotation encoding="application/x-tex">\forall</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord">∀</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center">\nabla</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∇</mi></mrow><annotation encoding="application/x-tex">\nabla</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">∇</span></span></span></span></td>
<td style="text-align:center">\oiint</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∯</mo></mrow><annotation encoding="application/x-tex">\oiint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.111em;vertical-align:-0.306em;"></span><span class="mop vlist-t vlist-t2" style="position:relative;top:-0.0005000000000000282em;"><span class="vlist-r"><span class="vlist" style="height:0.8049999999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;">∬</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="overlay" style="height:0.499em;width:0.957em;"><svg width='0.957em' height='0.499em' style='width:0.957em' viewBox='0 0 957 499' preserveAspectRatio='xMinYMin'><path d='M512.6 71.6c272.6 0 320.3 106.8 320.3 178.2 0 70.8-47.7 177.6
-320.3 177.6S193.1 320.6 193.1 249.8c0-71.4 46.9-178.2 319.5-178.2z
m368.1 178.2c0-86.4-60.9-215.4-368.1-215.4-306.4 0-367.3 129-367.3 215.4 0 85.8
60.9 214.8 367.3 214.8 307.2 0 368.1-129 368.1-214.8z'/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.306em;"><span></span></span></span></span></span></span></span></td>
<td style="text-align:center">\exists</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∃</mi></mrow><annotation encoding="application/x-tex">\exists</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord">∃</span></span></span></span></td>
</tr>
</tbody>
</table>
<h2 id="常用表示"><a class="markdownIt-Anchor" href="#常用表示"></a> 常用表示</h2>
<table>
<thead>
<tr>
<th style="text-align:center">语法</th>
<th style="text-align:center">表示</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">表示</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><code>\vec{A}</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo>⃗</mo></mover></mrow><annotation encoding="application/x-tex">\vec{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9663299999999999em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9663299999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.09660999999999997em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center"><code>\hat{A}</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9467699999999999em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9467699999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.11110999999999999em;">^</span></span></span></span></span></span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center"><code>\bar{A}</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo>ˉ</mo></mover></mrow><annotation encoding="application/x-tex">\bar{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8201099999999999em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8201099999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.11110999999999999em;">ˉ</span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center"><code>\ddot{A}</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo>¨</mo></mover></mrow><annotation encoding="application/x-tex">\ddot{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9201900000000001em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.11110999999999999em;">¨</span></span></span></span></span></span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center"><code>\hbar</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">ℏ</mi></mrow><annotation encoding="application/x-tex">\hbar</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68889em;vertical-align:0em;"></span><span class="mord">ℏ</span></span></span></span></td>
<td style="text-align:center"><code>\sqrt[n]{a}</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mroot><mi>a</mi><mi>n</mi></mroot></mrow><annotation encoding="application/x-tex">\sqrt[n]{a}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.23972em;"></span><span class="mord sqrt"><span class="root"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.5516160000000001em;"><span style="top:-2.836336em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size6 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span></span></span></span><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8002800000000001em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathdefault">a</span></span></span><span style="top:-2.76028em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,
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</tr>
<tr>
<td style="text-align:center"><code>\overline{a+b}</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{a+b}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.97777em;vertical-align:-0.08333em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.89444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">b</span></span></span><span style="top:-3.81444em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.08333em;"><span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center"><code>^4_2He</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mrow></mrow><mn>2</mn><mn>4</mn></msubsup><mi>H</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">^4_2He</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0622159999999998em;vertical-align:-0.24810799999999997em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-2.4518920000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em;"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="mord mathdefault">e</span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center"><code>\sum_{i=0}^na_n</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></msubsup><msub><mi>a</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\sum_{i=0}^na_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104002em;vertical-align:-0.29971000000000003em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center"><code>\sum\limits_a^b</code></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mo>∑</mo><mi>a</mi><mi>b</mi></msubsup></mrow><annotation encoding="application/x-tex">\sum\limits_a^b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4861180000000003em;vertical-align:-0.950005em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.536113em;"><span style="top:-2.149995em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.950005em;"><span></span></span></span></span></span></span></span></span></td>
</tr>
</tbody>
</table>
<h3 id="矩阵表示"><a class="markdownIt-Anchor" href="#矩阵表示"></a> 矩阵表示</h3>
<figure class="highlight gauss"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><code class="hljs gauss">\begin{<span class="hljs-keyword">matrix</span>}<br>a & b\\<br>c & d<br>\<span class="hljs-keyword">end</span>{<span class="hljs-keyword">matrix</span>}<br></code></pre></td></tr></table></figure>
<table>
<thead>
<tr>
<th style="text-align:center"><strong>matrix</strong></th>
<th style="text-align:center"><strong>pmartix</strong></th>
<th style="text-align:center"><strong>bmartix</strong></th>
<th style="text-align:center"><strong>Bmartix</strong></th>
<th style="text-align:center"><strong>vmartix</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{matrix} a & b\\c & d\end{matrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4000000000000004em;vertical-align:-0.9500000000000004em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">(</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\begin{pmatrix} a & b\\c & d\end{pmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><annotation encoding="application/x-tex">\begin{bmatrix} a & b\\c & d\end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">]</span></span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\begin{Bmatrix} a & b\\c & d\end{Bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">}</span></span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">∣</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><mo fence="true">∣</mo></mrow><annotation encoding="application/x-tex">\begin{vmatrix} a & b\\c & d\end{vmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.424em;vertical-align:-0.9500199999999999em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.47398em;"><span style="top:-1.65598em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-2.26198em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-3.47398em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500199999999999em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.47398em;"><span style="top:-1.65598em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-2.26198em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-3.47398em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500199999999999em;"><span></span></span></span></span></span></span></span></span></span></span></td>
</tr>
</tbody>
</table>
<figure class="highlight llvm"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><code class="hljs llvm">\left(<br>\<span class="hljs-keyword">begin</span>{array}{<span class="hljs-keyword">cc</span>|<span class="hljs-keyword">c</span>} % l/<span class="hljs-keyword">c</span>/r means left/center/right<br>a & b & <span class="hljs-keyword">c</span>\\ % <span class="hljs-keyword">cc</span>|<span class="hljs-keyword">c</span> means extended matrix (katex not support)<br>e & f & g<br>\<span class="hljs-keyword">end</span>{array}<br>\right)<br></code></pre></td></tr></table></figure>
<table>
<thead>
<tr>
<th style="text-align:center">()</th>
<th style="text-align:center">[]</th>
<th style="text-align:center">{}</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">(</mo><mtable rowspacing="0.15999999999999992em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>e</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>f</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>g</mi></mstyle></mtd></mtr></mtable><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\begin{array}{ccc}a & b & c\\e & f & g\end{array}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">e</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>e</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>f</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>g</mi></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><annotation encoding="application/x-tex">\left[\begin{array}{ccc}a & b & c\\e & f & g\end{array}\right]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">e</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">]</span></span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>e</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>f</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>g</mi></mstyle></mtd></mtr></mtable><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\left\{\begin{array}{ccc}a & b & c\\e & f & g\end{array}\right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">e</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">}</span></span></span></span></span></span></td>
</tr>
</tbody>
</table>
<h3 id="分段函数"><a class="markdownIt-Anchor" href="#分段函数"></a> 分段函数</h3>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnalign="center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">∣</mi><mi>x</mi><mi mathvariant="normal">∣</mi></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>x</mi><mo>≤</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>s</mi><mi>i</mi><mi>n</mi><mfrac><mn>1</mn><mi>x</mi></mfrac></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>x</mi><mo>></mo><mn>0</mn></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">f(x)=\left\{
\begin{array}{cc}
|x| & x\leq0 \\
sin \frac 1x & x>0
\end{array}\right.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.4051080000000002em;vertical-align:-0.9525540000000003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.452554em;"><span style="top:-3.612554em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">∣</span><span class="mord mathdefault">x</span><span class="mord">∣</span></span></span><span style="top:-2.4074459999999998em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">s</span><span class="mord mathdefault">i</span><span class="mord mathdefault">n</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9525540000000003em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.452554em;"><span style="top:-3.612554em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span></span></span><span style="top:-2.4074459999999998em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9525540000000003em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
<figure class="highlight livescript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><code class="hljs livescript">f(x)=<span class="hljs-string">\left\{</span> % {需要`<span class="hljs-string">\`转义</span><br><span class="hljs-string">\begin{array}{lc}</span><br>|x| & x <span class="hljs-string">\leq</span> <span class="hljs-number">0</span> <span class="hljs-string">\\</span><br>sin <span class="hljs-string">\frac</span> <span class="hljs-number">1x</span> & x > <span class="hljs-number">0</span><br><span class="hljs-string">\end{array}\right.</span> % .替代不显示括号<br></code></pre></td></tr></table></figure>
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