Fixed diagonal matrix eigen decomposition to return eigenvectors as diagonal matrix

[OzgurMertEmir]

Solution to issue Eigen decomposition of Diagonal matrix returns Dense eigenvectors #53007. Modified the eigen function for diagonal matrices to return eigenvectors as diagonal matrices.

Closes #53007.

[jishnub]

You might need to update some tests that are explicitly checking for a dense matrix.

[dkarrasch]

This infers just fine:

julia> using LinearAlgebra

julia> using Test

julia> @inferred eigen(Diagonal(ones(3)))
Eigen{Float64, Float64, Diagonal{Float64, Vector{Float64}}, Vector{Float64}}
values:
3-element Vector{Float64}:
 1.0
 1.0
 1.0
vectors:
3×3 Diagonal{Float64, Vector{Float64}}:
 1.0   ⋅    ⋅ 
  ⋅   1.0   ⋅ 
  ⋅    ⋅   1.0

julia> @inferred eigvecs(Diagonal(ones(3)))
3×3 Diagonal{Float64, Vector{Float64}}:
 1.0   ⋅    ⋅ 
  ⋅   1.0   ⋅ 
  ⋅    ⋅   1.0

[dkarrasch]

The failing tests are unrelated. Thanks @OzgurMertEmir for picking this up, and welcome to the Julia community.