# An Elementary Proof of the Restricted Invertibility Theorem

 COMPUTER SCIENCE AND DISCRETE MATHEMATICS SEMINAR II Topic: An Elementary Proof of the Restricted Invertibility Theorem Speaker: Nikhil Srivastava Affiliation: Member, School of Mathematics Date: Tuesday, November 9 Time/Room: 10:30am - 12:30pm/S-101

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. Joint work with Dan Spielman.