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Author : Roger A. Horn,Charles R. Johnson
Publisher : Cambridge University Press
Page : 620 pages
File Size : 53,8 Mb
Release : 1994-06-24
Category : Mathematics
ISBN : 0521467136
This book treats several topics in matrix theory not included in its predecessor volume, Matrix Analysis.
Author : Roger A. Horn,Charles R. Johnson
Publisher : Cambridge University Press
Page : 580 pages
File Size : 48,5 Mb
Release : 1990-02-23
Category : Mathematics
ISBN : 0521386322
Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.
Author : Roger A. Horn,Charles R. Johnson
Publisher : Cambridge University Press
Page : 662 pages
File Size : 45,7 Mb
Release : 2012-10-22
Category : Mathematics
ISBN : 0521839408
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
Author : Terence Tao
Publisher : American Mathematical Society
Page : 296 pages
File Size : 44,6 Mb
Release : 2023-08-24
Category : Mathematics
ISBN : 9781470474591
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.
Author : Xian-Da Zhang
Publisher : Cambridge University Press
Page : 761 pages
File Size : 53,7 Mb
Release : 2017-10-05
Category : Computers
ISBN : 9781108417419
The theory, methods and applications of matrix analysis are presented here in a novel theoretical framework.
Author : Rajendra Bhatia
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 43,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461206538
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 : Fumio Hiai,Dénes Petz
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 52,8 Mb
Release : 2014-02-06
Category : Mathematics
ISBN : 9783319041506
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.
Author : Alan J. Laub
Publisher : SIAM
Page : 159 pages
File Size : 40,5 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 9780898715767
"Prerequisites for using this text are knowledge of calculus and some previous exposure to matrices and linear algebra, including, for example, a basic knowledge of determinants, singularity of matrices, eigenvalues and eigenvectors, and positive definite matrices. There are exercises at the end of each chapter."--BOOK JACKET.
Author : Fuzhen Zhang
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 43,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475757972
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.
Author : Charles R. Johnson,Ronald L. Smith,Michael J. Tsatsomeros
Publisher : Cambridge University Press
Page : 223 pages
File Size : 49,6 Mb
Release : 2020-10
Category : Mathematics
ISBN : 9781108478717
This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.
Author : R. A. Horn,C. R. Johnson
Publisher : Unknown
Page : 607 pages
File Size : 40,9 Mb
Release : 1999
Category : Electronic
ISBN : OCLC:824130339
Author : Carl D. Meyer
Publisher : SIAM
Page : 729 pages
File Size : 42,8 Mb
Release : 2000-06-01
Category : Mathematics
ISBN : 9780898714548
This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook.
Author : Sudipto Banerjee,Anindya Roy
Publisher : CRC Press
Page : 586 pages
File Size : 46,5 Mb
Release : 2014-06-06
Category : Mathematics
ISBN : 9781420095388
Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
Author : Charles R. Johnson
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 51,6 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821801543
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 : Stephan Ramon Garcia,Roger A. Horn
Publisher : Cambridge University Press
Page : 447 pages
File Size : 52,7 Mb
Release : 2017-05-11
Category : Mathematics
ISBN : 9781107103818
A second course in linear algebra for undergraduates in mathematics, computer science, physics, statistics, and the biological sciences.