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Published May 27, 2015 | Submitted
Journal Article Open

An Introduction to Matrix Concentration Inequalities

Tropp, Joel A.


Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.

Additional Information

© 2015 J. A. Tropp. ISBN: 978-1-60198-838-6 I gratefully acknowledge financial support from the Office of Naval Research under awards N00014-08-1-0883 and N00014-11-1002, the Air Force Office of Strategic Research under award FA9550-09-1-0643, and an Alfred P. Sloan Fellowship. Some of this research was completed at the Institute of Pure and Applied Mathematics at UCLA. I would also like to thank the California Institute of Technology and the Moore Foundation.

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August 20, 2023
August 20, 2023