A Simple Generalization of a Result for Random Matrices with Independent Sub-Gaussian Rows

TL;DR

This paper presents a straightforward generalization of a known result for random matrices with independent sub-Gaussian rows, expanding its applicability and illustrating its usefulness with an example.

Contribution

It offers a simple, broad generalization of Vershynin's theorem for sub-Gaussian matrices, enhancing theoretical understanding and practical utility.

Findings

Generalizes Vershynin's result for sub-Gaussian matrices

Provides an example demonstrating the generalization's usefulness

Simplifies the application of matrix concentration inequalities

Abstract

In this short note, we give a very simple but useful generalization of a result of Vershynin (Theorem 5.39 of [1]) for a random matrix with independent sub-Gaussian rows. We also explain with an example where our generalization is useful.