Tests for multiplications of Hermitian matrices (JuliaLang#38380)

stdlib/LinearAlgebra/test/symmetric.jl

@@ -697,4 +697,34 @@ end
  end
 end
 
+@testset "Dsiambiguation multiplication with transposed AbstractMatrix methods in linalg/matmul.jl for $T and $S" for T in
+ (Float16, Float32, Float64, BigFloat), S in (ComplexF16, ComplexF32, ComplexF64)
+ let Ahrs = Transpose(Hermitian(Symmetric(rand(T, 3, 3)))),
+ Acs = Transpose(Symmetric(rand(S, 3, 3))),
+ Ahcs = Transpose(Hermitian(Symmetric(rand(S, 3, 3))))
+
+ @test Ahrs * Ahrs ≈ Ahrs * parent(Ahrs)
+ @test Ahrs * Acs ≈ Ahrs * parent(Acs)
+ @test Acs * Acs ≈ parent(Acs) * parent(Acs)
+ @test Acs * Ahrs ≈ parent(Acs) * Ahrs
+ @test Ahrs * Ahcs ≈ parent(Ahrs) * Ahcs
+ @test Ahcs * Ahrs ≈ Ahcs * parent(Ahrs)
+ end
+end
+
+@testset "Dsiambiguation multiplication with adjointed AbstractMatrix methods in linalg/matmul.jl for $T and $S" for T in
+ (Float16, Float32, Float64, BigFloat), S in (ComplexF16, ComplexF32, ComplexF64)
+ let Ahrs = Adjoint(Hermitian(Symmetric(rand(T, 3, 3)))),
+ Acs = Adjoint(Symmetric(rand(S, 3, 3))),
+ Ahcs = Adjoint(Hermitian(Symmetric(rand(S, 3, 3))))
+
+ @test Ahrs * Ahrs ≈ Ahrs * parent(Ahrs)
+ @test Ahcs * Ahcs ≈ parent(Ahcs) * parent(Ahcs)
+ @test Ahrs * Ahcs ≈ Ahrs * parent(Ahcs)
+ @test Acs * Ahcs ≈ Acs * parent(Ahcs)
+ @test Ahcs * Ahrs ≈ parent(Ahcs) * Ahrs
+ @test Ahcs * Acs ≈ parent(Ahcs) * Acs
+ end
+end
+
 end # module TestSymmetric