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arXiv · 1206.5180

Invertibility of random matrices: unitary and orthogonal perturbations

Mark Rudelson·Roman Vershynin
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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.

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Mark Rudelson, Roman Vershynin. 2013-01-30. Invertibility of random matrices: unitary and orthogonal perturbations. https://arxiv.org/abs/1206.5180

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