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A Survey of Matrix Theory and Matrix Inequalities

Author: Marvin Marcus

Publisher: Courier Corporation

Published: 1992-01-01

Total Pages: 212

ISBN-13: 9780486671024

Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.

Matrix Inequalities

Author: Xingzhi Zhan

Publisher: Springer

Published: 2004-10-20

Total Pages: 124

ISBN-13: 3540454217

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The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.

An Introduction to Matrix Concentration Inequalities

Author: Joel Tropp

Publisher:

Published: 2015-05-27

Total Pages: 256

ISBN-13: 9781601988386

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Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore 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.

Linear Matrix Inequalities in System and Control Theory

Author: Stephen Boyd

Publisher: SIAM

Published: 1994-01-01

Total Pages: 203

ISBN-13: 9781611970777

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In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.

Matrix Analysis

Author: Rajendra Bhatia

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 360

ISBN-13: 1461206537

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This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.

Advances in Linear Matrix Inequality Methods in Control

Author: Laurent El Ghaoui

Publisher: SIAM

Published: 2000-01-01

Total Pages: 399

ISBN-13: 9780898719833

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Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control.

Matrix Inequalities and Their Extensions to Lie Groups

Author: Tin-Yau Tam

Publisher: CRC Press

Published: 2018-03-14

Total Pages: 148

ISBN-13: 0429889283

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Matrix Inequalities and Their Extensions to Lie Groups gives a systematic and updated account of recent important extensions of classical matrix results, especially matrix inequalities, in the context of Lie groups. It is the first systematic work in the area and will appeal to linear algebraists and Lie group researchers.

Matrix Theory

Author: Fuzhen Zhang

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 290

ISBN-13: 1475757972

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This volume concisely presents fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The only prerequisites are a decent background in elementary linear algebra and calculus.

Matrix Analysis

Author: Roger A. Horn

Publisher: Cambridge University Press

Published: 1990-02-23

Total Pages: 580

ISBN-13: 9780521386326

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Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.

A Dynamical Approach to Random Matrix Theory

Author: László Erdős

Publisher: American Mathematical Soc.

Published: 2017-08-30

Total Pages: 226

ISBN-13: 1470436485

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A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.