Year: 2008
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Rudelson, Mark, Vershynin, Roman
Institutions: University of Michigan, University of Missouri
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950268483