This is an announcement for the paper "On the restricted invertibility problem with an additional constraint for random matrices" by Stephane Chretien.

Abstract: The Restricted Invertibility problem is the problem of selecting the largest subset of columns of a given matrix $X$, while keeping the smallest singular value of the extracted submatrix above a certain threshold. In this paper, we address this problem in the simpler case where $X$ is a random matrix but with the additional constraint that the selected columns be almost orthogonal to a given vector $v$. Our main result is a lower bound on the number of columns we can extract from a normalized i.i.d. Gaussian matrix for the worst $v$.

Archive classification: math.PR math.FA

Submitted from: stephane.chretien@npl.co.uk

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1511.05463

or

http://arXiv.org/abs/1511.05463