Are eigenvectors of real symmetric or hermitian matrix computed from `eigen` all orthogonal

[stevengj]

@antoine-levitt

Btw I’m not sure whether it actually happens that ggev does give (very) non-orthonormal eigenvectors for (close to) hermitian matrices or if the non-hermitian solver tries to keep eigenvectors as orthogonal as they can be anyway for stability.

Since the algorithm starts by finding the Schur form, I think it follows that it should stay close to orthonormal for nearly Hermitian matrices (where the Schur form is nearly diagonal), even for repeated eigenvalues?