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

@article{BenaychGeorges2012TheSV,
  title={The singular values and vectors of low rank perturbations of large rectangular random matrices},
  author={Florent Benaych-Georges and Raj Rao Nadakuditi},
  journal={J. Multivariate Analysis},
  year={2012},
  volume={111},
  pages={120-135}
}
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. As in the prequel, where we considered the eigenvalues of Hermitian matrices, the non-random limiting value is shown to depend explicitly on the limiting singular value distribution of the… CONTINUE READING
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