On the singularity of random matrices with independent entries
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We consider n by n real matrices whose entries are non-degenerate random variables that are independent but non necessarily identically distributed, and show that the probability that such a matrix is singular is O(1/sqrt{n}). The purpose of this note is to provide a short and elementary proof of this fact using a Bernoulli decomposition of arbitrary non degenerate random variables.
to be published in the Proc. Amer. Math. Soc
to be published in the Proc. Amer. Math. Soc