Invertibility of random matrices: unitary and orthogonal perturbations
Probability
2014-03-05 v2
Abstract
We show that a perturbation of any fixed square matrix D by a random unitary matrix is well invertible with high probability. A similar result holds for perturbations by random orthogonal matrices; the only notable exception is when D is close to orthogonal. As an application, these results completely eliminate a hard-to-check condition from the Single Ring Theorem by Guionnet, Krishnapur and Zeitouni.
Keywords
Cite
@article{arxiv.1206.5180,
title = {Invertibility of random matrices: unitary and orthogonal perturbations},
author = {Mark Rudelson and Roman Vershynin},
journal= {arXiv preprint arXiv:1206.5180},
year = {2014}
}
Comments
46 pages. A more general result on orthogonal perturbations of complex matrices added. It rectified an inaccuracy in application to Single Ring Theorem for orthogonal matrices