fix eigvals,eigvecs,eigen for Diagonal{Matrix}

[fatteneder]

Fixes JuliaLang/LinearAlgebra.jl#594.

There has been another attempt on fixing this #31509, but that seemed to have stopped two years ago.

@stevengj @dkarrasch Since you were involved in the issue and the other PR, may I ask you to also review this?

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I hope I understood correctly how the fix in JuliaLang/LinearAlgebra.jl#594 was meant to work:
I implemented it such that the results of eigvals(D), eigvecs(D), eigen(D) behave as in the case with ordinary matrices, e.g.
if D is a block diagonal matrix then

julia> vals, vecs = eigen(D)
julia> D * vecs == vecs * Diagonal(vals) # true

Closes #31509.

[DilumAluthge]

Bump @dkarrasch @stevengj

[dkarrasch]

Sorry for the delay; I'll review this next. For the tests that involve multiplication, we should indeed have approximate tests. For tests of functionality where you know you've only shuffled exact data around, exact tests are fine.

[dkarrasch]

Some small comments, otherwise LGTM. The crucial thing was to be able to multiply the diagonal matrix of matrices with the eigenvector matrix. That works nicely, as the tests show.

[fatteneder]

Thank you for the review. Will try to update this soonish.

[dkarrasch]

Just in case: if you agree with the suggestions, you can switch to the "Files changed" tab, then "add suggestion to batch" for the agreed suggestions, and then push the commit. No need to get back to your own codebase.

[dkarrasch]

Thanks @fatteneder for your contribution!