An Elementary Proof of the Restricted Invertibility Theorem

Details An Elementary Proof of the Restricted Invertibility Theorem An Elementary Proof of the Restricted Invertibility Theorem

2009-11-05

arxiv.org/abs/0911.1114v4

Mathematics

Functional Analysis

submitted to Israel J. Math

Scientific paper

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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