Small ball probability for the condition number of random matrices

Alexander E. Litvak, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann

Let $A$ be an $n\times n$ random matrix with i.i.d. entries of zero mean, unit variance and a bounded subgaussian moment. We show that the condition number $s_{\max}(A)/s_{\min}(A)…