A Survey Of Matrix Theory And Matrix Inequalities
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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.
A Survey Of Matrix Theory And Matrix Inequalities
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Author : Marvin Marcus
language : en
Publisher:
Release Date : 2014-01-01
A Survey Of Matrix Theory And Matrix Inequalities written by Marvin Marcus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with categories.
Written for advanced undergraduate students, this highly regarded book presents an enormous amount of information in a concise and accessible format. Beginning with the assumption that the reader has never seen a matrix before, the authors go on to provide a survey of a substantial part of the field, including many areas of modern research interest. Part One of the book covers not only the standard ideas of matrix theory, but ones, as the authors state, "that reflect our own prejudices," among them Kronecker products, compound and induced matrices, quadratic relations, permanents, incidence matrices and generalizations of commutativity. Part Two begins with a survey of elementary properties of convex sets and polyhedra and presents a proof of the Birkhoff theorem on doubly stochastic matrices. This is followed by a discussion of the properties of convex functions and a list of classical inequalities. This material is then combined to yield many of the interesting matrix inequalities of Weyl, Fan, Kantorovich and others. The treatment is along the lines developed by these authors and their successors and many of their proofs are included. This chapter contains an account of the classical Perron Frobenius-Wielandt theory of indecomposable nonnegative matrices and ends with some important results on stochastic matrices. Part Three is concerned with a variety of results on the localization of the characteristic roots of a matrix in terms of simple functions of its entries or of entries of a related matrix. The presentation is essentially in historical order, and out of the vast number of results in this field the authors have culled those that seemed most interesting or useful. Readers will find many of the proofs of classical theorems and a substantial number of proofs of results in contemporary research literature.
A Survey Of Matrix Theory And Matrix Inequalities
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Author : Henryk Minc
language : en
Publisher:
Release Date : 1969
A Survey Of Matrix Theory And Matrix Inequalities written by Henryk Minc and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
Matrix Analysis
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Author : Rajendra Bhatia
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Matrix Analysis written by Rajendra Bhatia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
A good part of matrix theory is functional analytic in spirit. This statement can be turned around. There are many problems in operator theory, where most of the complexities and subtleties are present in the finite-dimensional case. My purpose in writing this book is to present a systematic treatment of methods that are useful in the study of such problems. This book is intended for use as a text for upper division and gradu ate courses. Courses based on parts of the material have been given by me at the Indian Statistical Institute and at the University of Toronto (in collaboration with Chandler Davis). The book should also be useful as a reference for research workers in linear algebra, operator theory, mathe matical physics and numerical analysis. A possible subtitle of this book could be Matrix Inequalities. A reader who works through the book should expect to become proficient in the art of deriving such inequalities. Other authors have compared this art to that of cutting diamonds. One first has to acquire hard tools and then learn how to use them delicately. The reader is expected to be very thoroughly familiar with basic lin ear algebra. The standard texts Finite-Dimensional Vector Spaces by P.R.
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 Linear Matrix Inequality Methods In Control
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Author : Laurent El Ghaoui
language : en
Publisher: SIAM
Release Date : 2000-01-01
Advances In Linear Matrix Inequality Methods In Control written by Laurent El Ghaoui and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
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.
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.
Matrix Analysis
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Author : Roger A. Horn
language : en
Publisher: Cambridge University Press
Release Date : 1990-02-23
Matrix Analysis written by Roger A. Horn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-02-23 with Mathematics categories.
In this book the authors present classical and recent results for matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematics, and the necessary material has only occurred sporadically in the literature and university curricula. As the interest in applied mathematics has grown, the need for a text and a reference work offering a broad selection of topics has become apparent, and this book aims to meet that need. This book will be welcomed as an undergraduate or graduate textbook for students studying matrix analysis. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. They begin with a review and discussion of eigenvalues and eigenvectors. The following chapters each treat a major topic in depth. This volume should be useful not only as a text, but also as a self-contained reference work to a variety of audiences in other scientific fields.
Matrix Theory And Applications
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Author : Charles R. Johnson
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Matrix Theory And Applications written by Charles R. Johnson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.