fix #29392: HermOrSym should preserve structure when scaled with Numb…

…ers. (#29469)

stdlib/LinearAlgebra/src/symmetric.jl

@@ -440,12 +440,13 @@ mul!(C::StridedMatrix{T}, A::StridedMatrix{T}, B::Hermitian{T,<:StridedMatrix})
 *(adjA::Adjoint{<:Any,<:RealHermSymComplexHerm}, B::AbstractTriangular) = adjA.parent * B
 *(A::AbstractTriangular, adjB::Adjoint{<:Any,<:RealHermSymComplexHerm}) = A * adjB.parent
 
-for T in (:Symmetric, :Hermitian), op in (:*, :/)
-    # Deal with an ambiguous case
-    @eval ($op)(A::$T, x::Bool) = ($T)(($op)(A.data, x), sym_uplo(A.uplo))
-    S = T == :Hermitian ? :Real : :Number
-    @eval ($op)(A::$T, x::$S) = ($T)(($op)(A.data, x), sym_uplo(A.uplo))
-end
+# Scaling with Number
+*(A::Symmetric, x::Number) = Symmetric(A.data*x, sym_uplo(A.uplo))
+*(x::Number, A::Symmetric) = Symmetric(x*A.data, sym_uplo(A.uplo))
+*(A::Hermitian, x::Real) = Hermitian(A.data*x, sym_uplo(A.uplo))
+*(x::Real, A::Hermitian) = Hermitian(x*A.data, sym_uplo(A.uplo))
+/(A::Symmetric, x::Number) = Symmetric(A.data/x, sym_uplo(A.uplo))
+/(A::Hermitian, x::Real) = Hermitian(A.data/x, sym_uplo(A.uplo))
 
 function factorize(A::HermOrSym{T}) where T
     TT = typeof(sqrt(oneunit(T)))

stdlib/LinearAlgebra/test/symmetric.jl

@@ -517,4 +517,48 @@ end
     @test Hermitian(A, :U)[1,1] == Hermitian(A, :L)[1,1] == real(A[1,1])
 end
 
+@testset "issue #29392: SymOrHerm scaled with Number" begin
+    R = rand(Float64, 2, 2); C = rand(ComplexF64, 2, 2)
+    # Symmetric * Real, Real * Symmetric
+    A = Symmetric(R); x = 2.0
+    @test (A * x)::Symmetric == (x * A)::Symmetric
+    A = Symmetric(C); x = 2.0
+    @test (A * x)::Symmetric == (x * A)::Symmetric
+    # Symmetric * Complex, Complex * Symmetrics
+    A = Symmetric(R); x = 2.0im
+    @test (A * x)::Symmetric == (x * A)::Symmetric
+    A = Symmetric(C); x = 2.0im
+    @test (A * x)::Symmetric == (x * A)::Symmetric
+    # Hermitian * Real, Real * Hermitian
+    A = Hermitian(R); x = 2.0
+    @test (A * x)::Hermitian == (x * A)::Hermitian
+    A = Hermitian(C); x = 2.0
+    @test (A * x)::Hermitian == (x * A)::Hermitian
+    # Hermitian * Complex, Complex * Hermitian
+    A = Hermitian(R); x = 2.0im
+    @test (A * x)::Matrix == (x * A)::Matrix
+    A = Hermitian(C); x = 2.0im
+    @test (A * x)::Matrix == (x * A)::Matrix
+    # Symmetric / Real
+    A = Symmetric(R); x = 2.0
+    @test (A / x)::Symmetric == Matrix(A) / x
+    A = Symmetric(C); x = 2.0
+    @test (A / x)::Symmetric == Matrix(A) / x
+    # Symmetric / Complex
+    A = Symmetric(R); x = 2.0im
+    @test (A / x)::Symmetric == Matrix(A) / x
+    A = Symmetric(C); x = 2.0im
+    @test (A / x)::Symmetric == Matrix(A) / x
+    # Hermitian / Real
+    A = Hermitian(R); x = 2.0
+    @test (A / x)::Hermitian == Matrix(A) / x
+    A = Hermitian(C); x = 2.0
+    @test (A / x)::Hermitian == Matrix(A) / x
+    # Hermitian / Complex
+    A = Hermitian(R); x = 2.0im
+    @test (A / x)::Matrix == Matrix(A) / x
+    A = Hermitian(C); x = 2.0im
+    @test (A / x)::Matrix == Matrix(A) / x
+end
+
 end # module TestSymmetric