On the singularity of random matrices with independent entries
Probability
2008-01-09 v1
Abstract
We consider n by n real matrices whose entries are non-degenerate random variables that are independent but non necessarily identically distributed, and show that the probability that such a matrix is singular is O(1/sqrt{n}). The purpose of this note is to provide a short and elementary proof of this fact using a Bernoulli decomposition of arbitrary non degenerate random variables.
Keywords
Cite
@article{arxiv.0801.1221,
title = {On the singularity of random matrices with independent entries},
author = {Laurent Bruneau and Francois Germinet},
journal= {arXiv preprint arXiv:0801.1221},
year = {2008}
}
Comments
to be published in the Proc. Amer. Math. Soc