The least singular value of a random square matrix is O(n^{-1/2})
Probability
2016-12-23 v1 Functional Analysis
Abstract
Let A be a matrix whose entries are real i.i.d. centered random variables with unit variance and suitable moment assumptions. Then the smallest singular value of A is of order n^{-1/2} with high probability. The lower estimate of this type was proved recently by the authors; in this note we establish the matching upper estimate.
Keywords
Cite
@article{arxiv.0805.3407,
title = {The least singular value of a random square matrix is O(n^{-1/2})},
author = {Mark Rudelson and Roman Vershynin},
journal= {arXiv preprint arXiv:0805.3407},
year = {2016}
}
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6 pages