On the singularity of random matrices with independent entries

Details On the singularity of random matrices with independent entries On the singularity of random matrices with independent entries

2008-01-08

arxiv.org/abs/0801.1221v1

Mathematics

Probability

to be published in the Proc. Amer. Math. Soc

Scientific paper

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.

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