# A Refined Non-asymptotic Tail Bound of Sub-Gaussian Matrix

## TL;DR

This paper derives a refined non-asymptotic tail bound for the largest singular value of sub-Gaussian matrices and applies it to Gaussian Toeplitz matrices, enhancing understanding of their spectral properties.

## Contribution

It provides a new, sharper tail bound for sub-Gaussian matrices and demonstrates its application to Gaussian Toeplitz matrices.

## Key findings

- Refined tail bound for sub-Gaussian matrices
- Application to Gaussian Toeplitz matrices
- Improved understanding of spectral edge behavior

## Abstract

In this paper, we obtain a refined non-asymptotic tail bound for the largest singular value (the soft edge) of sub-Gaussian matrix. As an application, we use the obtained theorem to compute the tail bound of the Gaussian Toeplitz matrix.