The smallest singular value of a random rectangular matrix
Probability
2016-12-23 v4 Functional Analysis
Abstract
We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed dimensions. For an N by n matrix A with independent and identically distributed subgaussian entries, the smallest singular value of A is at least of the order \sqrt{N} - \sqrt{n-1} with high probability. A sharp estimate on the probability is also obtained.
Cite
@article{arxiv.0802.3956,
title = {The smallest singular value of a random rectangular matrix},
author = {Mark Rudelson and Roman Vershynin},
journal= {arXiv preprint arXiv:0802.3956},
year = {2016}
}
Comments
33 pages. A few misprints corrected