Invertibility of random matrices: norm of the inverse


Let $A$ be an $n \times n$ matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of $A^{-1}$ does not exceed $Cn^{3/2}$ with probability close to $1$.


Mark Rudelson

Department of Mathematics
University of Missouri
Columbia, MO 65211
United States