Invertibility of random matrices: Unitary and orthogonal perturbations
Invertibility of random matrices: Unitary and orthogonal perturbations
复制标题
随机矩阵的可逆性：酉扰动和正交扰动
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Vershynin
中科院分区：
文献类型：
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作者：
M. Rudelson;R. Vershynin
作者(S)：Rudelson，Mark；Vershynin，Roman|摘要：我们证明了任意固定方阵D被随机酉阵扰动是大概率可逆的。类似的结果也适用于随机正交矩阵的扰动；唯一值得注意的例外是当D接近于正交时。作为应用，这些结果完全消除了Guion net、Krishnapur和Zeitouni的单环定理中难以检验的条件。
Author(s): Rudelson, Mark; Vershynin, Roman | 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.