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Matrices.md

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$$I = \begin{pmatrix} {1} & {0} & {0} & {0} \\ {0} & {1} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {1} \end{pmatrix}$$

$$R{x} = \begin{pmatrix} {1} & {0} & {0} & {0} \\ {0} & cos{\theta} & sin{\theta} & {0} \\ {0} & -sin{\theta} & cos{\theta} & {0} \\ {0} & {0} & {0} & {1} \end{pmatrix} { , } R{y} = \begin{pmatrix} cos {\theta} & {0} & -sin{\theta} & {0} \\ {0} & {1} & {0} & {0} \\ sin{\theta} & {0} & cos{\theta} & {0} \\ {0} & {0} & {0} & {1} \end{pmatrix} { , } R{z} = \begin{pmatrix} cos{\theta} & sin{\theta} &{0} &{0}\\ -sin{\theta} & cos{\theta} &{0} &{0}\\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {1} \end{pmatrix}$$

$$R = R{z}R{y}R{x} = \begin{pmatrix} R_{x} & R_{y} & R_{z} & {0} \\ U_{x} & U_{y} & U_{z} & {0} \\ F_{x} & F_{y} & F_{z} & {0} \\ {0} & {0} & {0} & {1} \end{pmatrix} , T = \begin{pmatrix} {1} & {0} & {0} & {0} \\ {0} & {1} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ T_{x} & T_{y} & T_{z} & {1} \end{pmatrix}$$

$$I = (RT)V \quad , V = (RT)^{-1}I $$

$$V^{-1} = M = RT = \begin{pmatrix} R_{x} & R_{y} & R_{z} & {0} \\ U_{x} & U_{y} & U_{z} & {0} \\ F_{x} & F_{y} & F_{z} & {0} \\ T_{x} & T_{y} & T_{z} & {1} \end{pmatrix}$$