Matrix Analysis

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Matrix Analysis

Roger A. Horn,Charles R. Johnson
Matrix Analysis Book PDF

Author : Roger A. Horn,Charles R. Johnson
Publisher : Cambridge University Press
Page : 662 pages
File Size : 52,6 Mb
Release : 2012-10-22
Category : Mathematics
ISBN : 0521839408

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Matrix Analysis by Roger A. Horn,Charles R. Johnson Pdf

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.

Matrix Analysis

Rajendra Bhatia
Matrix Analysis Book PDF

Author : Rajendra Bhatia
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 54,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461206538

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Matrix Analysis by Rajendra Bhatia Pdf

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.

Matrix Analysis

Roger A. Horn,Charles R. Johnson
Matrix Analysis Book PDF

Author : Roger A. Horn,Charles R. Johnson
Publisher : Cambridge University Press
Page : 580 pages
File Size : 42,5 Mb
Release : 1990-02-23
Category : Mathematics
ISBN : 0521386322

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Matrix Analysis by Roger A. Horn,Charles R. Johnson Pdf

Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.

Topics in Matrix Analysis

Roger A. Horn,Charles R. Johnson
Topics in Matrix Analysis Book PDF

Author : Roger A. Horn,Charles R. Johnson
Publisher : Cambridge University Press
Page : 620 pages
File Size : 43,7 Mb
Release : 1994-06-24
Category : Mathematics
ISBN : 0521467136

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Topics in Matrix Analysis by Roger A. Horn,Charles R. Johnson Pdf

This book treats several topics in matrix theory not included in its predecessor volume, Matrix Analysis.

Introduction to Matrix Analysis and Applications

Fumio Hiai,Dénes Petz
Introduction to Matrix Analysis and Applications Book PDF

Author : Fumio Hiai,Dénes Petz
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 40,5 Mb
Release : 2014-02-06
Category : Mathematics
ISBN : 9783319041506

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Introduction to Matrix Analysis and Applications by Fumio Hiai,Dénes Petz Pdf

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.

Matrix Analysis for Scientists and Engineers

Alan J. Laub
Matrix Analysis for Scientists and Engineers Book PDF

Author : Alan J. Laub
Publisher : SIAM
Page : 159 pages
File Size : 52,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 9780898715767

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Matrix Analysis for Scientists and Engineers by Alan J. Laub Pdf

"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.

Matrix Analysis and Applications

Xian-Da Zhang
Matrix Analysis and Applications Book PDF

Author : Xian-Da Zhang
Publisher : Cambridge University Press
Page : 761 pages
File Size : 51,8 Mb
Release : 2017-10-05
Category : Computers
ISBN : 9781108417419

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Matrix Analysis and Applications by Xian-Da Zhang Pdf

The theory, methods and applications of matrix analysis are presented here in a novel theoretical framework.

Fundamentals of Matrix Analysis with Applications

Edward Barry Saff,Arthur David Snider
Fundamentals of Matrix Analysis with Applications Book PDF

Author : Edward Barry Saff,Arthur David Snider
Publisher : John Wiley & Sons
Page : 407 pages
File Size : 48,8 Mb
Release : 2015-10-12
Category : Mathematics
ISBN : 9781118953655

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Fundamentals of Matrix Analysis with Applications by Edward Barry Saff,Arthur David Snider Pdf

An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.

Matrix Analysis and Applied Linear Algebra

Carl D. Meyer
Matrix Analysis and Applied Linear Algebra Book PDF

Author : Carl D. Meyer
Publisher : SIAM
Page : 729 pages
File Size : 47,6 Mb
Release : 2000-06-01
Category : Mathematics
ISBN : 9780898714548

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Matrix Analysis and Applied Linear Algebra by Carl D. Meyer Pdf

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.

Matrix Theory

Fuzhen Zhang
Matrix Theory Book PDF

Author : Fuzhen Zhang
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 43,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475757972

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Matrix Theory by Fuzhen Zhang Pdf

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.

Numerical Matrix Analysis

Ilse C. F. Ipsen
Numerical Matrix Analysis Book PDF

Author : Ilse C. F. Ipsen
Publisher : SIAM
Page : 135 pages
File Size : 53,8 Mb
Release : 2009-07-23
Category : Mathematics
ISBN : 9780898716764

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Numerical Matrix Analysis by Ilse C. F. Ipsen Pdf

Matrix analysis presented in the context of numerical computation at a basic level.

Matrix Analysis for Statistics

James R. Schott
Matrix Analysis for Statistics Book PDF

Author : James R. Schott
Publisher : John Wiley & Sons
Page : 547 pages
File Size : 47,6 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9781119092483

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Matrix Analysis for Statistics by James R. Schott Pdf

An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.

Linear Algebra and Matrix Analysis for Statistics

Sudipto Banerjee,Anindya Roy
Linear Algebra and Matrix Analysis for Statistics Book PDF

Author : Sudipto Banerjee,Anindya Roy
Publisher : CRC Press
Page : 586 pages
File Size : 53,6 Mb
Release : 2014-06-06
Category : Mathematics
ISBN : 9781420095388

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Linear Algebra and Matrix Analysis for Statistics by Sudipto Banerjee,Anindya Roy Pdf

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.

Matrix Analysis and Computations

Zhong-Zhi Bai,Jian-Yu Pan
Matrix Analysis and Computations Book PDF

Author : Zhong-Zhi Bai,Jian-Yu Pan
Publisher : SIAM
Page : 496 pages
File Size : 41,6 Mb
Release : 2021-09-09
Category : Mathematics
ISBN : 9781611976632

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Matrix Analysis and Computations by Zhong-Zhi Bai,Jian-Yu Pan Pdf

This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics

Linear Algebra and Matrix Theory

Robert R. Stoll
Linear Algebra and Matrix Theory Book PDF

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 290 pages
File Size : 50,5 Mb
Release : 2012-10-17
Category : Mathematics
ISBN : 9780486623184

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Linear Algebra and Matrix Theory by Robert R. Stoll Pdf

Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.