We discuss the question of rank of symmetric and non-symmetric matrices when the entries are i.i.d. non-degenerate random variables. In particular we show that for an $n \times n$ symmetric matrix the probability that it is singular is of the order $O(n^{- (1/4) + \epsilon})$. This is joint work with Paulo Manrique and Victor Perez-Abreu.

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Last updated: 09 Oct 2024