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Invertibility of random submatrices via tail-decoupling and a matrix Chernoff inequality

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  • Chrétien, Stéphane
  • Darses, Sébastien

Abstract

Let X be a n×p real matrix with coherence μ(X)=maxj≠j′|XjtXj′|. We present a simplified and improved study of the quasi-isometry property for most submatrices of X obtained by uniform column sampling. Our results depend on μ(X), the operator norm ‖X‖ and the dimensions with explicit constants, which improve the previously known values by a large factor. The analysis relies on a tail-decoupling argument, of independent interest, and a recent version of the Non-Commutative Chernoff inequality (NCCI).

Suggested Citation

  • Chrétien, Stéphane & Darses, Sébastien, 2012. "Invertibility of random submatrices via tail-decoupling and a matrix Chernoff inequality," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1479-1487.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1479-1487
    DOI: 10.1016/j.spl.2012.03.038
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