From 7300e8a348fa1db4b4d295894a133db84eebd9d2 Mon Sep 17 00:00:00 2001
From: Don van den Bergh <donvdbergh@hotmail.com>
Date: Wed, 10 Sep 2025 16:30:07 +0200
Subject: [PATCH 1/2] ensure inverse of Symmetric{<:,Diagonal} returns same
 type

---
 src/diagonal.jl   |  4 ++++
 src/symmetric.jl  |  1 +
 test/symmetric.jl | 15 +++++++++++++++
 3 files changed, 20 insertions(+)

diff --git a/src/diagonal.jl b/src/diagonal.jl
index e60fb009..63cff1c8 100644
--- a/src/diagonal.jl
+++ b/src/diagonal.jl
@@ -970,6 +970,10 @@ function inv(D::Diagonal{T}) where T
     Diagonal(Di)
 end
 
+# Ensure doubly wrapped matrices use efficient diagonal methods and return a Symmetric/Hermitian type
+inv(A::Symmetric{<:Number,<:Diagonal}) = Symmetric(inv(A.data), sym_uplo(A.uplo))
+inv(A::Hermitian{<:Number,<:Diagonal}) = Hermitian(inv(real(A.data)), sym_uplo(A.uplo))
+
 function pinv(D::Diagonal{T}) where T
     Di = similar(D.diag, typeof(inv(oneunit(T))))
     for i = 1:length(D.diag)
diff --git a/src/symmetric.jl b/src/symmetric.jl
index 2cc74763..d95c3dcd 100644
--- a/src/symmetric.jl
+++ b/src/symmetric.jl
@@ -987,6 +987,7 @@ See also [`hermitianpart!`](@ref) for the corresponding in-place operation.
     This function requires Julia 1.10 or later.
 """
 hermitianpart(A::AbstractMatrix, uplo::Symbol=:U) = Hermitian(_hermitianpart(A), uplo)
+hermitianpart(a::Number) = real(a)
 
 """
     hermitianpart!(A::AbstractMatrix, uplo::Symbol=:U) -> Hermitian
diff --git a/test/symmetric.jl b/test/symmetric.jl
index 707b392d..ae10618f 100644
--- a/test/symmetric.jl
+++ b/test/symmetric.jl
@@ -874,6 +874,21 @@ end
     @test det(Hermitian(A))::Float64 == det(A) == 0.0
 end
 
+@testset "issue #1437: inverse of Symmetric|Hermitian{<:Any,<:Diagonal} returns of Symmetric|Hermitian{<:Any,<:Diagonal}" begin
+    Dreal    = Diagonal(randn(3))
+    Dcomplex = Diagonal(randn(ComplexF64, 3))
+    # without wrapper
+    invDreal = inv(Dreal)
+    invDcomplex = inv(real(Dcomplex)) # because Hermitian implies a real diagonal
+    # with wrapper
+    SDreal = Symmetric(Dreal)
+    HDcomplex = Hermitian(Dcomplex)
+    @test inv(SDreal)::Symmetric{Float64,typeof(Dreal)} ≈ invDreal
+    @test inv(HDcomplex)::Hermitian{Float64,typeof(Dreal)} ≈ invDcomplex
+    Dcomplex[2,2] = 0
+    @test_throws SingularException inv(HDcomplex)
+end
+
 @testset "symmetric()/hermitian() for Numbers" begin
     @test LinearAlgebra.symmetric(1) == LinearAlgebra.symmetric(1, :U) == 1
     @test LinearAlgebra.symmetric_type(Int) == Int

From af1fe0094769e7f7dbf8241eeb77d5af553da732 Mon Sep 17 00:00:00 2001
From: Don van den Bergh <donvdbergh@hotmail.com>
Date: Fri, 12 Sep 2025 09:40:42 +0200
Subject: [PATCH 2/2] remove hermitianpart(a::Number)

---
 src/symmetric.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/symmetric.jl b/src/symmetric.jl
index d95c3dcd..2cc74763 100644
--- a/src/symmetric.jl
+++ b/src/symmetric.jl
@@ -987,7 +987,6 @@ See also [`hermitianpart!`](@ref) for the corresponding in-place operation.
     This function requires Julia 1.10 or later.
 """
 hermitianpart(A::AbstractMatrix, uplo::Symbol=:U) = Hermitian(_hermitianpart(A), uplo)
-hermitianpart(a::Number) = real(a)
 
 """
     hermitianpart!(A::AbstractMatrix, uplo::Symbol=:U) -> Hermitian