Invertibility of random matrices: norm of the inverse

TL;DR

This paper proves that for an n by n matrix with independent subgaussian entries, the inverse's operator norm is bounded by a constant times n^{3/2} with high probability, highlighting invertibility properties.

Contribution

It establishes a probabilistic bound on the inverse norm of random matrices with subgaussian entries, advancing understanding of their invertibility behavior.

Findings

Operator norm of A^{-1} is at most Cn^{3/2} with high probability

Provides probabilistic bounds for invertibility of subgaussian random matrices

Enhances theoretical understanding of random matrix invertibility

Abstract

Let A be an n by 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.