When the eigenvalues for no two eigenvectors are the same, we get nice properties like symmetry and erthogonality(for hermetian). Which of these properties don't hold when some of them are degenerate?
2026-03-26 16:10:25.1774541425
Consequences of degenerate eigenvectors
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In the Hermitian case everything is still nice. From the theoretical point of view, the only bad thing is that there now exist non-orthogonal eigenbases, but you can nevertheless select an orthogonal eigenbasis yourself. There are also issues with numerics; I can elaborate on that if you are interested.
In the non-Hermitian case things can get hairy.