The condition number of a randomly perturbed matrix

Authors:
Van H. Vu;Terence Tao
Affiliations:
Rutgers, Piscataway, NJ;UCLA, Los Angeles, CA
Venue:
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Year:
2007

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Abstract

Let M be an arbitrary n by n matrix. We study the conditionnumber a random perturbation M+Nn of M, where Nn is arandom matrix. It is shown that, under very general conditions on M and Mn, the condition number of M+Nn is polynomial in nwith very high probability. The main novelty here is that we allow Nn to have discrete distribution.