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I am mainly interested in eigenvalue pertubations in rank-one modifications (especially for the smallest eigenvalue). Nearly all threads which I found consider rank-one modifications of symmetric matrices (1, 2).

  1. Are there results for non-symmetric matrices equivalent to the theorem of courant-fischer ?
  2. Can anyone provide literature which considers eigenvalue pertubation of non-symmetric matrices?

Greetings, Vincent

zinsinho
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  • There cannot be strict results about perturbation of eigenvalues for non symmetric matrices because they are too erratic. Already a rank one perturbation of a normal orthogonal matrix can bring all the eigenvalues to zero. The equivalent of courant-fisher on non symmetric matrices studies what happens to the singular values, not the eigenvalues – Exodd Jun 05 '24 at 13:12

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