Smallest singular value of a random rectangular matrix |
| |
| Authors: | Mark Rudelson Roman Vershynin |
| |
| Institution: | 1. University of Missouri, Department of Mathematics, Columbia, MO 65211;2. University of Michigan, Department of Mathematics, Ann Arbor, MI 48109 |
| |
| Abstract: | We prove an optimal estimate of the smallest singular value of a random sub‐Gaussian matrix, valid for all dimensions. For an N × n matrix A with independent and identically distributed sub‐Gaussian entries, the smallest singular value of A is at least of the order √N ? √n ? 1 with high probability. A sharp estimate on the probability is also obtained. © 2009 Wiley Periodicals, Inc. |
| |
| Keywords: | |
|
|
