diff --git a/stdlib/LinearAlgebra/src/symmetric.jl b/stdlib/LinearAlgebra/src/symmetric.jl
index 5ac664babff5d..6f778629b51b7 100644
--- a/stdlib/LinearAlgebra/src/symmetric.jl
+++ b/stdlib/LinearAlgebra/src/symmetric.jl
@@ -422,8 +422,8 @@ Base.copy(A::Adjoint{<:Any,<:Symmetric}) =
 Base.copy(A::Transpose{<:Any,<:Hermitian}) =
     Hermitian(copy(transpose(A.parent.data)), ifelse(A.parent.uplo == 'U', :L, :U))
 
-tr(A::Symmetric) = tr(A.data) # to avoid AbstractMatrix fallback (incl. allocations)
-tr(A::Hermitian) = real(tr(A.data))
+tr(A::Symmetric{<:Number}) = tr(A.data) # to avoid AbstractMatrix fallback (incl. allocations)
+tr(A::Hermitian{<:Number}) = real(tr(A.data))
 
 Base.conj(A::Symmetric) = Symmetric(parentof_applytri(conj, A), sym_uplo(A.uplo))
 Base.conj(A::Hermitian) = Hermitian(parentof_applytri(conj, A), sym_uplo(A.uplo))
diff --git a/stdlib/LinearAlgebra/test/symmetric.jl b/stdlib/LinearAlgebra/test/symmetric.jl
index b2fc9214f1ca4..23556c6548742 100644
--- a/stdlib/LinearAlgebra/test/symmetric.jl
+++ b/stdlib/LinearAlgebra/test/symmetric.jl
@@ -978,4 +978,15 @@ end
     @test conj(H) == conj(Array(H))
 end
 
+@testset "tr for block matrices" begin
+    m = [1 2; 3 4]
+    for b in (m, m * (1 + im))
+        M = fill(b, 3, 3)
+        for ST in (Symmetric, Hermitian)
+            S = ST(M)
+            @test tr(S) == sum(diag(S))
+        end
+    end
+end
+
 end # module TestSymmetric