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.
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..