Author : Marvin Marcus
Publisher : Courier Corporation
Page : 212 pages
File Size : 36,54 MB
Release : 1992-01-01
Category : 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 : Joel Tropp
Publisher :
Page : 256 pages
File Size : 18,82 MB
Release : 2015-05-27
Category : 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 : Stephen Boyd
Publisher : SIAM
Page : 203 pages
File Size : 13,32 MB
Release : 1994-01-01
Category : 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 : Laurent El Ghaoui
Publisher : SIAM
Page : 399 pages
File Size : 37,52 MB
Release : 2000-01-01
Category : 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 : Rajendra Bhatia
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 18,49 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461206537
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.
Author : Roger A. Horn
Publisher : Cambridge University Press
Page : 580 pages
File Size : 12,94 MB
Release : 1990-02-23
Category : Mathematics
ISBN : 9780521386326
Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.
Author : Charles R. Johnson
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 23,76 MB
Release : 1990
Category : Mathematics
ISBN : 0821801546
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.
Author : Stéphane Boucheron
Publisher : Oxford University Press
Page : 492 pages
File Size : 14,6 MB
Release : 2013-02-07
Category : Mathematics
ISBN : 0199535256
Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented.
Author : Albert W. Marshall
Publisher : Springer Science & Business Media
Page : 919 pages
File Size : 47,27 MB
Release : 2010-11-25
Category : Mathematics
ISBN : 0387682767
This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. ... This work is a valuable resource!” (Mathematical Reviews). “The authors ... present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of ... Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.
Author : Fumio Hiai
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 42,59 MB
Release : 2014-02-06
Category : Mathematics
ISBN : 3319041509
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.
