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arXiv · 1511.05463

On the restricted invertibility problem with an additional orthogonality constraint for random matrices

Stephane Chretien
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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 $v$.

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Stephane Chretien. 2015-12-04. On the restricted invertibility problem with an additional orthogonality constraint for random matrices. https://arxiv.org/abs/1511.05463

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