Inconsistency in `eigen` interface for specialised methods

[st--]

Some of the implementations such as eigen(::SymTridiagonal) don't actually accept the keyword arguments of the other implementations, scale, permute, sortby. (eigen(::Diagonal) does accept even permute and scale though it just ignores them.)

Should these also wrap the Lapack result in sorteig! before passing it to the Eigen constructor? And have dummy kwargs for scale and permute?

Originally posted by @st-- in JuliaLang/julia#43904 (comment)

[stevengj]

This is documented in the eigen docstring:

Some special matrix types (e.g. Diagonal or SymTridiagonal) may implement their own sorting convention and not accept a sortby keyword.

and

For general nonsymmetric matrices [emphasis added] it is possible to specify how the matrix is balanced before the eigenvector calculation. […documentation for permute and scale…]

For example, re-ordering the eigenvalues of a Diagonal matrix is a pretty awkward thing to do, because it makes the eigenvectors no longer the identity matrix. See also the discussion in JuliaLang/julia#21598