A Survey Of Matrix Theory And Matrix Inequalities
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A Survey of Matrix Theory and Matrix Inequalities
Author | : Marvin Marcus,Henryk Minc |
Publsiher | : Courier Corporation |
Total Pages | : 212 |
Release | : 1992-01-01 |
Genre | : Mathematics |
ISBN | : 048667102X |
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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.
Matrix Inequalities
Author | : Xingzhi Zhan |
Publsiher | : Springer |
Total Pages | : 124 |
Release | : 2004-10-20 |
Genre | : Mathematics |
ISBN | : 9783540454212 |
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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.
Linear Matrix Inequalities in System and Control Theory
Author | : Stephen Boyd,Laurent El Ghaoui,Eric Feron,Venkataramanan Balakrishnan |
Publsiher | : SIAM |
Total Pages | : 203 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 1611970776 |
Download Linear Matrix Inequalities in System and Control Theory Book in PDF, Epub and Kindle
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 Inequalities for Iterative Systems
Author | : Hanjo Taubig |
Publsiher | : CRC Press |
Total Pages | : 144 |
Release | : 2017-02-03 |
Genre | : Mathematics |
ISBN | : 9781351679091 |
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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 Theory
Author | : Fuzhen Zhang |
Publsiher | : Springer Science & Business Media |
Total Pages | : 290 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9781475757972 |
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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 Inequalities and Their Extensions to Lie Groups
Author | : Tin-Yau Tam,Xuhua Liu |
Publsiher | : CRC Press |
Total Pages | : 148 |
Release | : 2018-03-14 |
Genre | : Mathematics |
ISBN | : 9780429889288 |
Download Matrix Inequalities and Their Extensions to Lie Groups Book in PDF, Epub and Kindle
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.
Topics in Random Matrix Theory
Author | : Terence Tao |
Publsiher | : American Mathematical Soc. |
Total Pages | : 298 |
Release | : 2012-03-21 |
Genre | : Mathematics |
ISBN | : 9780821874301 |
Download Topics in Random Matrix Theory Book in PDF, Epub and Kindle
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
An Introduction to Matrix Concentration Inequalities
Author | : Joel Tropp |
Publsiher | : Unknown |
Total Pages | : 256 |
Release | : 2015-05-27 |
Genre | : Computers |
ISBN | : 1601988389 |
Download An Introduction to Matrix Concentration Inequalities Book in PDF, Epub and Kindle
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.