On low rank perturbation of matrices

Details On low rank perturbation of matrices On low rank perturbation of matrices

2008-02-26

arxiv.org/abs/0802.3874v2

Mathematics

Functional Analysis

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Scientific paper

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.

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