Given a matrix $A\in\mathbb{R}^{m\times n}$ with entries of $A$ being sampled i.i.d. from $\text{Bernoulli}(\alpha)$, where $\alpha\in(0,1)$ is a fixed constant. This paper (2nd sentence below equation (2)) claims that if $m=n$, then $A$ will be invertible with high probability. May I know why this is true for any $\alpha\in(0,1)$, or can anyone point me to a reference/result that states that this is true? I am asking since this claim doesn't seem very obvious to me. Thanks.
2026-02-23 10:23:41.1771842221
Why are square Bernoulli matrices invertible with high probability?
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