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