2008/02/26 by Lev Glebsky, Glebsky, Lev, Luis Manuel Rivera +1
Mathematics · #15A03 #15A18 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:15A03 #msc:15A18
paper · pdf · doi:10.48550/arxiv.0802.3874
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..
arxiv created 2008/09/02 · arxiv updated 2009/12/01
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.