English

On low rank perturbation of matrices

Functional Analysis 2008-09-02 v2

Abstract

The article is devoted to different aspects of the question "What can be done with a matrix by low rank perturbation?" It is proved that one can change a geometrically simple spectrum drastically by a rank 1 permutation, but the situation is quite different if one restricts oneself to normal matrices. Also, the Jordan normal form of a perturbed matrix is considered. It is proved that with respect to rank as a distance all almost unitary matrices are near unitary.

Keywords

Cite

@article{arxiv.0802.3874,
  title  = {On low rank perturbation of matrices},
  author = {Lev Glebsky and Luis Manuel Rivera},
  journal= {arXiv preprint arXiv:0802.3874},
  year   = {2008}
}

Comments

This is essentially a new paper, has new results and cites. When we were writing the previous version we were not aware about some related works and results..

R2 v1 2026-06-21T10:16:08.153Z