On singular values of matrices with independent rows

Abstract

We present deviation inequalities of random operators of the form $N^{-1}{\sum }_{i=1}^N{X}_i\otimes X_i$ from the average operator $E(X\otimes X)$, where $X_i$ are independent random vectors distributed as $X$, which is a random vector in $R^n$ or in ${\ell }_2$. We use these inequalities to estimate the singular values of random matrices with independent rows (without assuming that the entries are independent).