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I am using ARPACK's zndrv1 to diagonalise a matrix (the context is quantum chemistry). While all vectors have a norm 1, as expected, vectors corresponding to degenerate eigenstates aren't always orthogonal (often their inner product will be roughly 0.01).

Are there any parameters I can adjust to improve orthonormality (even if it means longer compute time)?

I understand there are alternative libraries and routines out there. I am specifically curious about ARPACK.

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  • $\begingroup$ Are these vectors orthogonal with the non-degenerate ones? $\endgroup$ – nicoguaro Mar 24 at 13:57
  • $\begingroup$ Yes. Their inner product is typically on the order of magnitude of 1e-8 to 1e-13, which is more than enough accuracy for my purposes. $\endgroup$ – DJames Mar 24 at 21:49
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    $\begingroup$ What happens if you orthogonalize (e.g. by Modified Gram-Schmidt) the vectors that you've gotten from ARPACK associated with the null eigenvalues? Are the resulting eigenvectors usable? $\endgroup$ – Brian Borchers Mar 24 at 22:35

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