Download or read book A Survey of Matrix Theory and Matrix Inequalities written by Marvin Marcus and published by Courier Corporation. This book was released on 1992-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Inequalities written by Xingzhi Zhan and published by Springer. This book was released on 2004-10-19 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Matrix Inequalities in System and Control Theory written by Stephen Boyd and published by SIAM. This book was released on 1994-01-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Inequalities and Their Extensions to Lie Groups written by Tin-Yau Tam and published by CRC Press. This book was released on 2018-03-14 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Matrix Concentration Inequalities written by Joel Tropp and published by . This book was released on 2015-05-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Analysis written by Rajendra Bhatia and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Theory written by Fuzhen Zhang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Linear Matrix Inequality Methods in Control written by Laurent El Ghaoui and published by SIAM. This book was released on 2000-01-01 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Matrix Inequalities written by Mohammad Bagher Ghaemi and published by Springer Nature. This book was released on 2021-07-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Inequalities for Iterative Systems written by Hanjo Taubig and published by CRC Press. This book was released on 2017-02-03 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Analysis written by Roger A. Horn and published by Cambridge University Press. This book was released on 1990-02-23 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.
Download or read book Matrix Theory and Applications written by Charles R. Johnson and published by American Mathematical Soc.. This book was released on 1990 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.
Download or read book A Dynamical Approach to Random Matrix Theory written by László Erdős and published by American Mathematical Soc.. This book was released on 2017-08-30 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topics in Matrix Analysis written by Roger A. Horn and published by Cambridge University Press. This book was released on 1994-06-24 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics in matrix theory not included in the previous volume, but with important applications and of special mathematical interest. As with the previous volume, the authors assume a background knowledge of elementary linear algebra and rudimentary analytical concepts. Many examples and exercises of varying difficulty are included.
Download or read book Introduction to Matrix Analysis and Applications written by Fumio Hiai and published by Springer Science & Business Media. This book was released on 2014-02-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Download or read book Topics in Random Matrix Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2012-03-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Matrix Analysis written by Richard Bellman and published by SIAM. This book was released on 1997-12-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lucid and concise, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods.
