An Introduction to Matrix Concentration Inequalities

TL;DR

This paper introduces matrix concentration inequalities, a powerful set of tools that simplify complex problems in random matrix theory, making advanced results more accessible for computational mathematics applications.

Contribution

It provides a comprehensive overview of the most successful methods in matrix concentration inequalities and illustrates their applications through interesting examples.

Findings

Simplifies complex random matrix problems

Demonstrates effectiveness of concentration inequalities

Provides accessible methods for computational mathematics

Abstract

In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix concentration inequalities, research has advanced to the point where we can conquer many (formerly) challenging problems with a page or two of arithmetic. The aim of this monograph is to describe the most successful methods from this area along with some interesting examples that these techniques can illuminate.