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An elementary proof of the restricted invertibility theorem

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Abstract

We give an elementary proof of a generalization of Bourgain and Tzafriri’s Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for finding the desired subspace.

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Authors and Affiliations

  1. Department of Computer Science, Program in Applied Mathematics, Yale University, New Haven, CT, 06520, USA

    Daniel A. Spielman

  2. Department of Computer Science, Yale University, PO Box 208285, New Haven, CT, 06520, USA

    Nikhil Srivastava

Authors
  1. Daniel A. Spielman
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  2. Nikhil Srivastava
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Corresponding author

Correspondence to Daniel A. Spielman.

Additional information

This material is based upon work supported by the National Science Foundation under grants CCF-0634904, CCF-0634957 and CCF-0915487. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Spielman, D.A., Srivastava, N. An elementary proof of the restricted invertibility theorem. Isr. J. Math. 190, 83–91 (2012). https://doi.org/10.1007/s11856-011-0194-2

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  • DOI: https://doi.org/10.1007/s11856-011-0194-2

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