Invertibility of random matrices: Unitary and orthogonal perturbations
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- by Mark Rudelson and Roman Vershynin
- J. Amer. Math. Soc. 27 (2014), 293-338
- DOI: https://doi.org/10.1090/S0894-0347-2013-00771-7
- Published electronically: May 8, 2013
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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.References
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Bibliographic Information
- Mark Rudelson
- Affiliation: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109
- MR Author ID: 243851
- Email: rudelson@umich.edu
- Roman Vershynin
- Affiliation: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109
- MR Author ID: 636015
- Email: romanv@umich.edu
- Received by editor(s): June 22, 2012
- Received by editor(s) in revised form: January 30, 2013
- Published electronically: May 8, 2013
- Additional Notes: The first author was partially supported by NSF grant DMS 1161372
The second author was partially supported by NSF grant DMS 1001829. - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 27 (2014), 293-338
- MSC (2010): Primary 60B20
- DOI: https://doi.org/10.1090/S0894-0347-2013-00771-7
- MathSciNet review: 3164983
Dedicated: In memory of Joram Lindenstrauss