Matrix Inequalities
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| Author | : Xingzhi Zhan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 138 |
| Release | : 2002-07-09 |
| Genre | : Mathematics |
| ISBN | : 9783540437987 |
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.
| Author | : Marvin Marcus |
| Publisher | : Courier Corporation |
| Total Pages | : 212 |
| Release | : 1992-01-01 |
| Genre | : Mathematics |
| ISBN | : 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.
| Author | : Stephen Boyd |
| Publisher | : SIAM |
| Total Pages | : 203 |
| Release | : 1994-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970777 |
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.
| Author | : Xingzhi Zhan |
| Publisher | : Springer |
| Total Pages | : 127 |
| Release | : 2004-10-19 |
| Genre | : Mathematics |
| ISBN | : 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.
| Author | : Mohammad Bagher Ghaemi |
| Publisher | : Springer Nature |
| Total Pages | : 287 |
| Release | : 2021-07-11 |
| Genre | : Mathematics |
| ISBN | : 3030760472 |
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.
| Author | : Laurent El Ghaoui |
| Publisher | : SIAM |
| Total Pages | : 399 |
| Release | : 2000-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898719833 |
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.
| Author | : Joel Tropp |
| Publisher | : |
| Total Pages | : 256 |
| Release | : 2015-05-27 |
| Genre | : Computers |
| ISBN | : 9781601988386 |
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.
| Author | : Hanjo Taubig |
| Publisher | : CRC Press |
| Total Pages | : 219 |
| Release | : 2017-02-03 |
| Genre | : Mathematics |
| ISBN | : 1498777791 |
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.
| Author | : Tin-Yau Tam |
| Publisher | : CRC Press |
| Total Pages | : 148 |
| Release | : 2018-03-14 |
| Genre | : Mathematics |
| ISBN | : 0429889283 |
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.
| Author | : Kazuo Tanaka |
| Publisher | : John Wiley & Sons |
| Total Pages | : 321 |
| Release | : 2004-04-07 |
| Genre | : Science |
| ISBN | : 0471465224 |
A comprehensive treatment of model-based fuzzy control systems This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications. Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model. This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field. Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.
