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Matrix Inequalities

Author: Xingzhi Zhan

Publisher: Springer

Published: 2004-10-19

Total Pages: 127

ISBN-13: 3540454217

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.

A Survey of Matrix Theory and Matrix Inequalities

Author: Marvin Marcus

Publisher: Courier Corporation

Published: 1992-01-01

Total Pages: 212

ISBN-13: 9780486671024

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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.

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.

Advances in Matrix Inequalities

Author: Mohammad Bagher Ghaemi

Publisher: Springer Nature

Published: 2021-07-11

Total Pages: 287

ISBN-13: 3030760472

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This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.

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.

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 for Iterative Systems

Author: Hanjo Taubig

Publisher: CRC Press

Published: 2017-02-03

Total Pages: 144

ISBN-13: 1351679090

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The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.

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 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.

Mathematical Methods for Robust and Nonlinear Control

Author: Matthew C. Turner

Publisher: Springer Science & Business Media

Published: 2007-10-23

Total Pages: 444

ISBN-13: 1848000251

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The underlying theory on which much modern robust and nonlinear control is based can be difficult to grasp. This volume is a collection of lecture notes presented by experts in advanced control engineering. The book is designed to provide a better grounding in the theory underlying several important areas of control. It is hoped the book will help the reader to apply otherwise abstruse ideas of nonlinear control in a variety of real systems.