Matrix Inequalities
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Matrix Inequalities
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Author : Xingzhi Zhan
language : en
Publisher: Springer
Release Date : 2004-10-19
Matrix Inequalities written by Xingzhi Zhan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.
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.
Linear Matrix Inequalities In System And Control Theory
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Author : Stephen Boyd
language : en
Publisher: SIAM
Release Date : 1994-01-01
Linear Matrix Inequalities In System And Control Theory written by Stephen Boyd and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
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.
A Survey Of Matrix Theory And Matrix Inequalities
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Author : Marvin Marcus
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
A Survey Of Matrix Theory And Matrix Inequalities written by Marvin Marcus and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
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.
A Survey Of Matrix Theory And Matrix Inequalities
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Author : Marvin Marcus
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
A Survey Of Matrix Theory And Matrix Inequalities written by Marvin Marcus and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
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.
An Introduction To Matrix Concentration Inequalities
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Author : Joel Tropp
language : en
Publisher:
Release Date : 2015-05-27
An Introduction To Matrix Concentration Inequalities written by Joel Tropp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-27 with Computers categories.
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 Matrix Inequalities
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Author : Mohammad Bagher Ghaemi
language : en
Publisher: Springer Nature
Release Date : 2021-07-11
Advances In Matrix Inequalities written by Mohammad Bagher Ghaemi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-11 with Mathematics categories.
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.
Matrix Inequalities And Their Extensions To Lie Groups
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Author : Tin-Yau Tam
language : en
Publisher: CRC Press
Release Date : 2018-03-14
Matrix Inequalities And Their Extensions To Lie Groups written by Tin-Yau Tam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-14 with Mathematics categories.
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.
Differential Linear Matrix Inequalities
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Author : José C. Geromel
language : en
Publisher: Springer Nature
Release Date : 2023-06-21
Differential Linear Matrix Inequalities written by José C. Geromel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-21 with Technology & Engineering categories.
This book is entirely devoted to sampled-data control systems analysis and design from a new point of view, which has at its core a mathematical tool named Differential Linear Matrix Inequality - DLMI, a natural generalization of Linear Matrix Inequality - LMI, that had an important and deep impact on systems and control theory almost thirty years ago. It lasts until now. It is shown that the DLMI is well adapted to deal with the important class of sampled-data control systems in both theoretical and numerical contexts. All design conditions are expressed by convex programming problems, including when robustness against parameter uncertainty is assessed and imposed through state feedback control. Special attention is given to filter, dynamic output feedback and model predictive control design, as well as nonlinear systems of Lur’e class and Markov jump linear systems. The subject is treated with mathematical rigor, at the same time, trying to keep the reading agreeable and fruitful for colleagues and students. To this respect, the book contains together with the theoretical developments, many solved illustrative examples and the formulation of some open problems that could be faced and hopefully solved by interested readers.
Matrix Inequalities For Iterative Systems
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Author : Hanjo Taubig
language : en
Publisher: CRC Press
Release Date : 2017-02-03
Matrix Inequalities For Iterative Systems written by Hanjo Taubig and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-03 with Mathematics categories.
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.
Geometry Of Linear Matrix Inequalities
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Author : Tim Netzer
language : en
Publisher: Springer Nature
Release Date : 2023-06-07
Geometry Of Linear Matrix Inequalities written by Tim Netzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-07 with Mathematics categories.
This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can be represented and approximated as spectrahedra and their shadows (projections). Several general results obtained in the last 15 years by a variety of different methods are presented in the book, along with the necessary background from algebra and geometry.