Additional tests for #49533: Hermitian symmetric matrices.

stdlib/LinearAlgebra/test/symmetric.jl

@@ -825,6 +825,7 @@ end
 end
 
 @testset "issue #49533" begin
+    # Real valued
     A = Float64[1 1 0 0; 1 2 1 0; 0 1 3 1; 0 0 1 4] ;
     B = Matrix(Diagonal(Float64[1:4;])) ;
     # eigen
@@ -836,6 +837,21 @@ end
     # eigvals
     @test eigvals(A, B) ≈ eigvals(A, Symmetric(B))
     @test eigvals(A, B) ≈ eigvals(Symmetric(A), B)
+    # Complex valued
+    A =  [1.0+im 1.0+1.0im 0 0; 1.0+1.0im 2.0+3.0im 1.0+1.0im 0; 0 1.0+2.0im 3.0+4.0im 1.0+5.0im; 0 0 1.0+1.0im 4.0+4.0im] ;
+    A = (A+A')/2 ;
+    B =  [2.0+2.0im 1.0+1.0im 4.0+4.0im 3.0+3.0im; 0 3.0+2.0im 1.0+1.0im 3.0+4.0im; 3.0+3.0im 1.0+4.0im 0 0; 0 1.0+2.0im 3.0+1.0im 1.0+1.0im];
+    B = (B+B')/2 ; 
+    # eigen
+    sf = x->(real(x),imag(x))
+    e0,v0 = eigen(A, B; sortby=sf)
+    e1,v1 = eigen(A, Hermitian(B); sortby=sf)
+    e2,v2 = eigen(Hermitian(A), B; sortby=sf)
+    @test e0 ≈ e1 && v0 ≈ v1
+    @test e0 ≈ e2 && v0 ≈ v2
+    # eigvals
+    @test eigvals(A, B; sortby=sf) ≈ eigvals(A, Hermitian(B); sortby=sf)
+    @test eigvals(A, B; sortby=sf) ≈ eigvals(Hermitian(A), B; sortby=sf)
 end
 
 end # module TestSymmetric