The condition number of a randomly perturbed matrix
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the condition number distribution of complex wishart matrices
IEEE Transactions on Communications
The Exact Distribution of the Condition Number of a Gaussian Matrix
SIAM Journal on Matrix Analysis and Applications
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Let $\kappa$ be the condition number of an $m$-by-$n$ matrix with independent standard Gaussian entries, either real ($\beta = 1$) or complex ($\beta = 2$). The major result is the existence of a constant $C$ (depending on $m$, $n$, and $\beta$) such that $P[\kappa x]