Random perturbation of low rank matrices: Improving classical bounds
Abstract
Matrix perturbation inequalities, such as Weyl's theorem (concerning the singular values) and the Davis-Kahan theorem (concerning the singular vectors), play essential roles in quantitative science; in particular, these bounds have found application in data analysis as well as related areas of engineering and computer science. In many situations, the perturbation is assumed to be random, and the original matrix has certain structural properties (such as having low rank). We show that, in this scenario, classical perturbation results, such as Weyl and Davis-Kahan, can be improved significantly. We believe many of our new bounds are close to optimal and also discuss some applications.
Keywords
Cite
@article{arxiv.1311.2657,
title = {Random perturbation of low rank matrices: Improving classical bounds},
author = {Sean O'Rourke and Van Vu and Ke Wang},
journal= {arXiv preprint arXiv:1311.2657},
year = {2023}
}
Comments
28 pages, 1 figure. Updated introduction and references. Final version. Wrong replacement in [v6]