The singular values and vectors of low rank perturbations of large rectangular random matrices

Florent Benaych-Georges and Raj Rao Nadakuditi

Journal of Multivariate Analysis, 2012, vol. 111, issue C, 120-135

Abstract: In this paper, we consider the singular values and singular vectors of finite, low rank perturbations of large rectangular random matrices. Specifically, we prove almost sure convergence of the extreme singular values and appropriate projections of the corresponding singular vectors of the perturbed matrix.

Keywords: Random matrices; Haar measure; Free probability; Phase transition; Random eigenvalues; Random eigenvectors; Random perturbation; Sample covariance matrices (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (16)

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DOI: 10.1016/j.jmva.2012.04.019

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