The least singular value of a random square matrix is [formula omitted

Abstract

Let A be a matrix whose entries are real i.i.d. centered random variables with unit variance and suitable moment assumptions. Then the smallest singular value s n ( A ) is of order n − 1 / 2 with high probability. The lower estimate of this type was proved recently by the authors; in this Note we establish the matching upper estimate. To cite this article: M. Rudelson, R. Vershynin, C. R. Acad. Sci. Paris, Ser. I 346 (2008).