Matrix Deviation Inequality for $\ell_{p}$-Norm

TL;DR

This paper investigates the universality of matrix deviation inequalities for p-norms, demonstrating that these inequalities hold for sub-Gaussian matrices, extending known results from Gaussian matrices.

Contribution

It establishes the universality of matrix deviation inequalities for p-norms with sub-Gaussian matrices, broadening the scope beyond Gaussian ensembles.

Findings

Matrix deviation inequality holds for p-norm with sub-Gaussian matrices.

Universality property extends from Gaussian to sub-Gaussian matrices.

Provides theoretical foundation for p-norm analysis in diverse random matrix models.

Abstract

Motivated by the general matrix deviation inequality for i.i.d ensemble Gaussian matrix, we study its universality property. As a starting point for this problem, we show that this property holds for $\ell_{p}$-norm with $1\leq p< \infty$ and i.i.d ensemble sub-Gaussian random matrix, which is a random matrix with i.i.d mean-zero, unit variance, sub-Gaussian entries.