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Introduction to Matrix Concentration Inequalities
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266 b
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This book is designed to bring random matrix theory to the people. In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical methods for studying random matrices 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. This book describes the most successful methods from this area along with some interesting examples that these techniques can illuminate. The results in these pages are intended to inspire future work on applications of random matrices as well as refinements of the matrix concentration inequalities discussed herein. The book presents a coherent body of results that are based on a generalization of the classical Laplace transform method for establishing scalar concentration inequalities.
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