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

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  • Benaych-Georges, Florent
  • Nadakuditi, Raj Rao

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.

Suggested Citation

  • Benaych-Georges, Florent & Nadakuditi, Raj Rao, 2012. "The singular values and vectors of low rank perturbations of large rectangular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 120-135.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:120-135
    DOI: 10.1016/j.jmva.2012.04.019
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    7. Pan, Guangming, 2010. "Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1330-1338, July.
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