The condition number of a randomly perturbed matrix

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.

Locations

• arXiv (Cornell University) - PDF
• arXiv (Cornell University) - View
• arXiv (Cornell University) - PDF
• arXiv (Cornell University) - View