Translator Disclaimer
2015 Sharp lower bounds on the least singular value of a random matrix without the fourth moment condition
Pavel Yaskov
Author Affiliations +
Electron. Commun. Probab. 20: 1-9 (2015). DOI: 10.1214/ECP.v20-4089

Abstract

We obtain non-asymptotic lower bounds on the least singular value of ${\mathbf X}_{pn}^\top/\sqrt{n}$, where ${\mathbf X}_{pn}$ is a $p\times n$ random matrix whose columns are independent copies of an isotropic random vector $X_p$ in $ {\mathbb R}^p$. We assume that there exist $M>0$ and $\alpha\in\leqslant M/t^{2+\alpha}$ for all $t>0$ and any unit vector $v\in{\mathbb R}^p$. These bounds depend on $y=p/n,$ $\alpha$, $M$ and are asymptotically optimal up to a constant factor.

Citation

Download Citation

Pavel Yaskov. "Sharp lower bounds on the least singular value of a random matrix without the fourth moment condition." Electron. Commun. Probab. 20 1 - 9, 2015. https://doi.org/10.1214/ECP.v20-4089

Information

Accepted: 10 June 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1318.60009
MathSciNet: MR3358966
Digital Object Identifier: 10.1214/ECP.v20-4089

Subjects:
Primary: 60B20

JOURNAL ARTICLE
9 PAGES


SHARE
Back to Top