## PIMS-Math Analysis Seminar: Pierre Youssef

- Date: 11/28/2013
- Time: 15:00

*U. Alberta*

University of British Columbia

Extracting a large well-coniditoned block inside a matrix

Given U an nÃ—m matrix, the aim is to extract a large number of linearly independent columns of U and estimate the smallest and the largest singular value of the restricted matrix. For that, we give two deterministic algorithms: one for a normalized version of the restricted invertibility principle of Bourgain-Tzafriri, and one for the norm of coordinate restriction problem due to Kashin-Tzafriri. Merging the two algorithms, we are able to extract a well-conditioned block inside U, improving a previous result due to Vershynin. We give some applications of this result to the study of contact points of a convex body.

Location: Math Annex 1118