diff --git a/Project.toml b/Project.toml
index a7851a45..ec1efe36 100644
--- a/Project.toml
+++ b/Project.toml
@@ -55,3 +55,6 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
 test = ["Aqua", "JET", "SafeTestsets", "Test", "TestExtras", "ChainRulesCore", "ChainRulesTestUtils", "StableRNGs", "Zygote", "CUDA", "AMDGPU", "GenericLinearAlgebra", "GenericSchur", "Mooncake"]
+
+[sources]
+CUDA = {url="https://github.com/juliagpu/cuda.jl", rev="master"}
diff --git a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
index 04bee40e..a7830914 100644
--- a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
+++ b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
@@ -128,17 +128,23 @@ function MatrixAlgebraKit._project_hermitian_diag!(A::StridedROCMatrix, B::Strid
 end
 
 MatrixAlgebraKit.ishermitian_exact(A::StridedROCMatrix) = all(A .== adjoint(A))
-MatrixAlgebraKit.ishermitian_exact(A::Diagonal{T, <:StridedROCVector{T}}) where {T} =
-    all(A.diag .== adjoint(A.diag))
+MatrixAlgebraKit.ishermitian_exact(A::Diagonal{T, <:StridedROCVector{T}}) where {T <: Real} = true
+function MatrixAlgebraKit.ishermitian_exact(A::Diagonal{T, <:StridedROCVector{T}}) where {T <: Complex}
+    return all(isreal.(A.diag))
+end
 MatrixAlgebraKit.ishermitian_approx(A::StridedROCMatrix; kwargs...) =
     @invoke MatrixAlgebraKit.ishermitian_approx(A::Any; kwargs...)
 
 MatrixAlgebraKit.isantihermitian_exact(A::StridedROCMatrix) =
     all(A .== -adjoint(A))
-MatrixAlgebraKit.isantihermitian_exact(A::Diagonal{T, <:StridedROCVector{T}}) where {T} =
-    all(A.diag .== -adjoint(A.diag))
+MatrixAlgebraKit.isantihermitian_exact(A::Diagonal{T, <:StridedROCVector{T}}) where {T <: Real} = all(iszero(A.diag))
+MatrixAlgebraKit.isantihermitian_exact(A::Diagonal{T, <:StridedROCVector{T}}) where {T <: Complex} =
+    all(iszero.(real.(A.diag)))
 MatrixAlgebraKit.isantihermitian_approx(A::StridedROCMatrix; kwargs...) =
     @invoke MatrixAlgebraKit.isantihermitian_approx(A::Any; kwargs...)
+function MatrixAlgebraKit.isantihermitian_approx(A::Diagonal{T, <:StridedROCVector{T}}; atol, rtol, kwargs...) where {T <: Real}
+    return sum(abs2, A.diag) ≤ max(atol, rtol * norm(A))
+end
 
 function MatrixAlgebraKit._avgdiff!(A::StridedROCMatrix, B::StridedROCMatrix)
     axes(A) == axes(B) || throw(DimensionMismatch())
diff --git a/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl b/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl
index e4c77453..c681d3eb 100644
--- a/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl
+++ b/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl
@@ -153,17 +153,23 @@ end
 
 MatrixAlgebraKit.ishermitian_exact(A::StridedCuMatrix) =
     all(A .== adjoint(A))
-MatrixAlgebraKit.ishermitian_exact(A::Diagonal{T, <:StridedCuVector{T}}) where {T} =
-    all(A.diag .== adjoint(A.diag))
+MatrixAlgebraKit.ishermitian_exact(A::Diagonal{T, <:StridedCuVector{T}}) where {T <: Real} = true
+function MatrixAlgebraKit.ishermitian_exact(A::Diagonal{T, <:StridedCuVector{T}}) where {T <: Complex}
+    return all(isreal.(A.diag))
+end
 MatrixAlgebraKit.ishermitian_approx(A::StridedCuMatrix; kwargs...) =
     @invoke MatrixAlgebraKit.ishermitian_approx(A::Any; kwargs...)
 
 MatrixAlgebraKit.isantihermitian_exact(A::StridedCuMatrix) =
     all(A .== -adjoint(A))
-MatrixAlgebraKit.isantihermitian_exact(A::Diagonal{T, <:StridedCuVector{T}}) where {T} =
-    all(A.diag .== -adjoint(A.diag))
+MatrixAlgebraKit.isantihermitian_exact(A::Diagonal{T, <:StridedCuVector{T}}) where {T <: Real} = all(iszero(A.diag))
+MatrixAlgebraKit.isantihermitian_exact(A::Diagonal{T, <:StridedCuVector{T}}) where {T <: Complex} =
+    all(iszero.(real.(A.diag)))
 MatrixAlgebraKit.isantihermitian_approx(A::StridedCuMatrix; kwargs...) =
     @invoke MatrixAlgebraKit.isantihermitian_approx(A::Any; kwargs...)
+function MatrixAlgebraKit.isantihermitian_approx(A::Diagonal{T, <:StridedCuVector{T}}; atol, rtol, kwargs...) where {T <: Real}
+    return sum(abs2, A.diag) ≤ max(atol, rtol * norm(A))
+end
 
 function MatrixAlgebraKit._avgdiff!(A::StridedCuMatrix, B::StridedCuMatrix)
     axes(A) == axes(B) || throw(DimensionMismatch())
diff --git a/src/MatrixAlgebraKit.jl b/src/MatrixAlgebraKit.jl
index d3a04741..493f3a91 100644
--- a/src/MatrixAlgebraKit.jl
+++ b/src/MatrixAlgebraKit.jl
@@ -3,7 +3,7 @@ module MatrixAlgebraKit
 using LinearAlgebra: LinearAlgebra
 using LinearAlgebra: norm # TODO: eleminate if we use VectorInterface.jl?
 using LinearAlgebra: mul!, rmul!, lmul!, adjoint!, rdiv!, ldiv!
-using LinearAlgebra: sylvester, lu!
+using LinearAlgebra: sylvester, lu!, diagm
 using LinearAlgebra: isposdef, issymmetric
 using LinearAlgebra: Diagonal, diag, diagind, isdiag
 using LinearAlgebra: UpperTriangular, LowerTriangular
diff --git a/src/implementations/projections.jl b/src/implementations/projections.jl
index 8baf09a5..054b5b77 100644
--- a/src/implementations/projections.jl
+++ b/src/implementations/projections.jl
@@ -9,13 +9,15 @@ copy_input(::typeof(project_isometric), A) = copy_input(left_polar, A)
 
 function check_input(::typeof(project_hermitian!), A::AbstractMatrix, B::AbstractMatrix, ::AbstractAlgorithm)
     LinearAlgebra.checksquare(A)
-    n = Base.require_one_based_indexing(A)
+    Base.require_one_based_indexing(A)
+    n = size(A, 1)
     B === A || @check_size(B, (n, n))
     return nothing
 end
 function check_input(::typeof(project_antihermitian!), A::AbstractMatrix, B::AbstractMatrix, ::AbstractAlgorithm)
     LinearAlgebra.checksquare(A)
-    n = Base.require_one_based_indexing(A)
+    Base.require_one_based_indexing(A)
+    n = size(A, 1)
     B === A || @check_size(B, (n, n))
     return nothing
 end
@@ -61,6 +63,15 @@ function project_isometric!(A::AbstractMatrix, W, alg::AbstractAlgorithm)
     return W
 end
 
+function project_hermitian_native!(A::Diagonal, B::Diagonal, ::Val{anti}; kwargs...) where {anti}
+    if anti
+        diagview(A) .= imag.(diagview(B)) .* im
+    else
+        diagview(A) .= real.(diagview(B))
+    end
+    return A
+end
+
 function project_hermitian_native!(A::AbstractMatrix, B::AbstractMatrix, anti::Val; blocksize = 32)
     n = size(A, 1)
     for j in 1:blocksize:n
diff --git a/src/implementations/svd.jl b/src/implementations/svd.jl
index c8b27f3f..ef0c2bc3 100644
--- a/src/implementations/svd.jl
+++ b/src/implementations/svd.jl
@@ -356,6 +356,7 @@ function svd_full!(A::AbstractMatrix, USVᴴ, alg::GPU_SVDAlgorithm)
 
     return USVᴴ
 end
+svd_full!(A::Diagonal, USVᴴ, alg::GPU_SVDAlgorithm) = svd_full!(diagm(A.diag), USVᴴ, alg)
 
 function svd_trunc!(A::AbstractMatrix, USVᴴ, alg::TruncatedAlgorithm{<:GPU_Randomized})
     check_input(svd_trunc!, A, USVᴴ, alg.alg)
@@ -373,6 +374,7 @@ function svd_trunc!(A::AbstractMatrix, USVᴴ, alg::TruncatedAlgorithm{<:GPU_Ran
 
     return Utr, Str, Vᴴtr, ϵ
 end
+svd_trunc!(A::Diagonal, USVᴴ, alg::GPU_SVDAlgorithm) = svd_trunc!(diagm(A.diag), USVᴴ, alg)
 
 function svd_compact!(A::AbstractMatrix, USVᴴ, alg::GPU_SVDAlgorithm)
     check_input(svd_compact!, A, USVᴴ, alg)
@@ -396,6 +398,7 @@ function svd_compact!(A::AbstractMatrix, USVᴴ, alg::GPU_SVDAlgorithm)
 
     return USVᴴ
 end
+svd_compact!(A::Diagonal, USVᴴ, alg::GPU_SVDAlgorithm) = svd_compact!(diagm(A.diag), USVᴴ, alg)
 _argmaxabs(x) = reduce(_largest, x; init = zero(eltype(x)))
 _largest(x, y) = abs(x) < abs(y) ? y : x
 
@@ -418,3 +421,10 @@ function svd_vals!(A::AbstractMatrix, S, alg::GPU_SVDAlgorithm)
 
     return S
 end
+function svd_vals!(A::Diagonal, S, alg::GPU_SVDAlgorithm)
+    check_input(svd_vals!, A, S, alg)
+    Ad = diagview(A)
+    S .= abs.(Ad)
+    sort!(S; rev = true)
+    return S
+end
diff --git a/test/amd/projections.jl b/test/amd/projections.jl
index b22148e2..cab09206 100644
--- a/test/amd/projections.jl
+++ b/test/amd/projections.jl
@@ -12,37 +12,41 @@ const BLASFloats = (Float32, Float64, ComplexF32, ComplexF64)
     m = 54
     noisefactor = eps(real(T))^(3 / 4)
     for alg in (NativeBlocked(blocksize = 16), NativeBlocked(blocksize = 32), NativeBlocked(blocksize = 64))
-        A = ROCArray(randn(rng, T, m, m))
-        Ah = (A + A') / 2
-        Aa = (A - A') / 2
-        Ac = copy(A)
+        for A in (ROCArray(randn(rng, T, m, m)), Diagonal(ROCArray(randn(rng, T, m))))
+            Ah = (A + A') / 2
+            Aa = (A - A') / 2
+            Ac = copy(A)
 
-        Bh = project_hermitian(A, alg)
-        @test ishermitian(Bh)
-        @test Bh ≈ Ah
-        @test A == Ac
-        Bh_approx = Bh + noisefactor * Aa
-        @test !ishermitian(Bh_approx)
-        @test ishermitian(Bh_approx; rtol = 10 * noisefactor)
+            Bh = project_hermitian(A, alg)
+            @test ishermitian(Bh)
+            @test Bh ≈ Ah
+            @test A == Ac
+            # this is still hermitian for real Diagonals!
+            Bh_approx = Bh + noisefactor * Aa
+            if !isa(A, Diagonal) && !(T <: Real)
+                @test !ishermitian(Bh_approx)
+            end
+            @test ishermitian(Bh_approx; rtol = 10 * noisefactor)
 
-        Ba = project_antihermitian(A, alg)
-        @test isantihermitian(Ba)
-        @test Ba ≈ Aa
-        @test A == Ac
-        Ba_approx = Ba + noisefactor * Ah
-        @test !isantihermitian(Ba_approx)
-        @test isantihermitian(Ba_approx; rtol = 10 * noisefactor)
+            Ba = project_antihermitian(A, alg)
+            @test isantihermitian(Ba)
+            @test Ba ≈ Aa
+            @test A == Ac
+            Ba_approx = Ba + noisefactor * Ah
+            @test !isantihermitian(Ba_approx)
+            @test isantihermitian(Ba_approx; rtol = 10 * noisefactor)
 
-        Bh = project_hermitian!(Ac, alg)
-        @test Bh === Ac
-        @test ishermitian(Bh)
-        @test Bh ≈ Ah
+            Bh = project_hermitian!(Ac, alg)
+            @test Bh === Ac
+            @test ishermitian(Bh)
+            @test Bh ≈ Ah
 
-        copy!(Ac, A)
-        Ba = project_antihermitian!(Ac, alg)
-        @test Ba === Ac
-        @test isantihermitian(Ba)
-        @test Ba ≈ Aa
+            copy!(Ac, A)
+            Ba = project_antihermitian!(Ac, alg)
+            @test Ba === Ac
+            @test isantihermitian(Ba)
+            @test Ba ≈ Aa
+        end
     end
 end
 
@@ -54,24 +58,25 @@ end
         svdalgs = (ROCSOLVER_QRIteration(), ROCSOLVER_Jacobi())
         algs = (PolarViaSVD.(svdalgs)...,) # PolarNewton()) # TODO
         @testset "algorithm $alg" for alg in algs
-            A = ROCArray(randn(rng, T, m, n))
-            W = project_isometric(A, alg)
-            @test isisometric(W)
-            W2 = project_isometric(W, alg)
-            @test W2 ≈ W # stability of the projection
-            @test W * (W' * A) ≈ A
+            for A in (ROCArray(randn(rng, T, m, n)), Diagonal(ROCArray(randn(rng, T, m))))
+                W = project_isometric(A, alg)
+                @test isisometric(W)
+                W2 = project_isometric(W, alg)
+                @test W2 ≈ W # stability of the projection
+                @test W * (W' * A) ≈ A
 
-            Ac = similar(A)
-            W2 = @constinferred project_isometric!(copy!(Ac, A), W, alg)
-            @test W2 === W
-            @test isisometric(W)
+                Ac = similar(A)
+                W2 = @constinferred project_isometric!(copy!(Ac, A), W, alg)
+                @test W2 === W
+                @test isisometric(W)
 
-            # test that W is closer to A then any other isometry
-            for k in 1:10
-                δA = ROCArray(randn(rng, T, m, n))
-                W = project_isometric(A, alg)
-                W2 = project_isometric(A + δA / 100, alg)
-                @test norm(A - W2) > norm(A - W)
+                # test that W is closer to A then any other isometry
+                for k in 1:10
+                    δA = ROCArray(randn(rng, T, size(A)...))
+                    W = project_isometric(A, alg)
+                    W2 = project_isometric(A + δA / 100, alg)
+                    @test norm(A - W2) > norm(A - W)
+                end
             end
         end
     end
diff --git a/test/cuda/projections.jl b/test/cuda/projections.jl
index d9f7bd7f..9eb3d478 100644
--- a/test/cuda/projections.jl
+++ b/test/cuda/projections.jl
@@ -12,37 +12,41 @@ const BLASFloats = (Float32, Float64, ComplexF32, ComplexF64)
     m = 54
     noisefactor = eps(real(T))^(3 / 4)
     for alg in (NativeBlocked(blocksize = 16), NativeBlocked(blocksize = 32), NativeBlocked(blocksize = 64))
-        A = CuArray(randn(rng, T, m, m))
-        Ah = (A + A') / 2
-        Aa = (A - A') / 2
-        Ac = copy(A)
+        for A in (CuArray(randn(rng, T, m, m)), Diagonal(CuArray(randn(rng, T, m))))
+            Ah = (A + A') / 2
+            Aa = (A - A') / 2
+            Ac = copy(A)
 
-        Bh = project_hermitian(A, alg)
-        @test ishermitian(Bh)
-        @test Bh ≈ Ah
-        @test A == Ac
-        Bh_approx = Bh + noisefactor * Aa
-        @test !ishermitian(Bh_approx)
-        @test ishermitian(Bh_approx; rtol = 10 * noisefactor)
+            Bh = project_hermitian(A, alg)
+            @test ishermitian(Bh)
+            @test Bh ≈ Ah
+            @test A == Ac
+            # this is still hermitian for real Diagonals!
+            Bh_approx = Bh + noisefactor * Aa
+            if !isa(A, Diagonal) && !(T <: Real)
+                @test !ishermitian(Bh_approx)
+            end
+            @test ishermitian(Bh_approx; rtol = 10 * noisefactor)
 
-        Ba = project_antihermitian(A, alg)
-        @test isantihermitian(Ba)
-        @test Ba ≈ Aa
-        @test A == Ac
-        Ba_approx = Ba + noisefactor * Ah
-        @test !isantihermitian(Ba_approx)
-        @test isantihermitian(Ba_approx; rtol = 10 * noisefactor)
+            Ba = project_antihermitian(A, alg)
+            @test isantihermitian(Ba)
+            @test Ba ≈ Aa
+            @test A == Ac
+            Ba_approx = Ba + noisefactor * Ah
+            @test !isantihermitian(Ba_approx)
+            @test isantihermitian(Ba_approx; rtol = 10 * noisefactor)
 
-        Bh = project_hermitian!(Ac, alg)
-        @test Bh === Ac
-        @test ishermitian(Bh)
-        @test Bh ≈ Ah
+            Bh = project_hermitian!(Ac, alg)
+            @test Bh === Ac
+            @test ishermitian(Bh)
+            @test Bh ≈ Ah
 
-        copy!(Ac, A)
-        Ba = project_antihermitian!(Ac, alg)
-        @test Ba === Ac
-        @test isantihermitian(Ba)
-        @test Ba ≈ Aa
+            copy!(Ac, A)
+            Ba = project_antihermitian!(Ac, alg)
+            @test Ba === Ac
+            @test isantihermitian(Ba)
+            @test Ba ≈ Aa
+        end
     end
 end
 
@@ -54,24 +58,25 @@ end
         svdalgs = (CUSOLVER_SVDPolar(), CUSOLVER_QRIteration(), CUSOLVER_Jacobi())
         algs = (PolarViaSVD.(svdalgs)...,) # PolarNewton()) # TODO
         @testset "algorithm $alg" for alg in algs
-            A = CuArray(randn(rng, T, m, n))
-            W = project_isometric(A, alg)
-            @test isisometric(W)
-            W2 = project_isometric(W, alg)
-            @test W2 ≈ W # stability of the projection
-            @test W * (W' * A) ≈ A
+            for A in (CuArray(randn(rng, T, m, n)), Diagonal(CuArray(randn(rng, T, m))))
+                W = project_isometric(A, alg)
+                @test isisometric(W)
+                W2 = project_isometric(W, alg)
+                @test W2 ≈ W # stability of the projection
+                @test W * (W' * A) ≈ A
 
-            Ac = similar(A)
-            W2 = @constinferred project_isometric!(copy!(Ac, A), W, alg)
-            @test W2 === W
-            @test isisometric(W)
+                Ac = similar(A)
+                W2 = @constinferred project_isometric!(copy!(Ac, A), W, alg)
+                @test W2 === W
+                @test isisometric(W)
 
-            # test that W is closer to A then any other isometry
-            for k in 1:10
-                δA = CuArray(randn(rng, T, m, n))
-                W = project_isometric(A, alg)
-                W2 = project_isometric(A + δA / 100, alg)
-                @test norm(A - W2) > norm(A - W)
+                # test that W is closer to A then any other isometry
+                for k in 1:10
+                    δA = CuArray(randn(rng, T, size(A)...))
+                    W = project_isometric(A, alg)
+                    W2 = project_isometric(A + δA / 100, alg)
+                    @test norm(A - W2) > norm(A - W)
+                end
             end
         end
     end