On the singularity of random matrices with independent entries

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.

Locations

• Proceedings of the American Mathematical Society - View - PDF
• arXiv (Cornell University) - View