Geodesic
Invertibility of random matrices: Unitary and orthogonal perturbations
Rudelson, Mark1 ; Vershynin, Roman1
1Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109
Journal of the American Mathematical Society, Tome 27 (2014) no. 2, pp. 293-338
Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S0894-0347-2013-00771-7

Rudelson, Mark  1   ; Vershynin, Roman  1

1 Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109 
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Rudelson, Mark; Vershynin, Roman. Invertibility of random matrices: Unitary and orthogonal perturbations. Journal of the American Mathematical Society, Tome 27 (2014) no. 2, pp. 293-338. doi: 10.1090/S0894-0347-2013-00771-7

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