On low rank perturbation of matrices

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Glebsky, Lev
Rivera, Luis Manuel
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Abstract
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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.
Comment: 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..
Keywords
Mathematics - Functional Analysis, 15A03, 15A18
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