On the singularity of random matrices with independent entries

Bruneau, Laurent; Germinet, François

doi:10.1090/S0002-9939-08-09595-6

On the singularity of random matrices with independent entries
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by Laurent Bruneau and François Germinet PDF

Proc. Amer. Math. Soc. 137 (2009), 787-792 Request permission

Abstract:

We consider $n$ by $n$ real matrices whose entries are non-degenerate random variables that are independent but not necessarily identically distributed, and show that the probability that such a matrix is singular is $O(1/\sqrt {n})$. The purpose of this paper 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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