INVERTIBILITY OF RANDOM MATRICES: UNITARY AND ORTHOGONAL PERTURBATIONS
Skip to main content
eScholarship
Open Access Publications from the University of California

UC Irvine

UC Irvine Previously Published Works bannerUC Irvine

INVERTIBILITY OF RANDOM MATRICES: UNITARY AND ORTHOGONAL PERTURBATIONS

  • Author(s): Rudelson, Mark;
  • Vershynin, Roman
  • et al.
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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View