# Singularity of random Bernoulli matrices

### Abstract

For each $n$, let $M_n$ be an $n\times n$ random matrix with independent $\pm 1$ entries. We show that
$\mathbb{P}\{M_n$ is singular $\}=(1/2+o_n(1))^n$, which settles an old problem. Some generalizations are considered.

## Authors

Konstantin Tikhomirov

School of Mathematics, Georgia Institute of Technology, Atlanta, GA