Matrix Analysis

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Author: Roger A. Horn,Roger A Horn,Charles R. Johnson

Publisher: Cambridge University Press

ISBN: 9780521386326

Category: Mathematics

Page: 561

View: 4621

Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of 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 mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topics.

Topics in Matrix Analysis

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Author: Roger A. Horn,Charles R. Johnson

Publisher: Cambridge University Press

ISBN: 9780521467131

Category: Mathematics

Page: 607

View: 9501

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

Matrix Analysis

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Author: Rajendra Bhatia

Publisher: Springer Science & Business Media

ISBN: 1461206537

Category: Mathematics

Page: 349

View: 2550

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

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Author: Roger A. Horn,Charles R. Johnson

Publisher: Cambridge University Press

ISBN: 0521839408

Category: Business & Economics

Page: 643

View: 7146

The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises.

Introduction to Matrix Analysis

Second Edition

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Author: Richard Bellman

Publisher: SIAM

ISBN: 0898713994

Category: Mathematics

Page: 403

View: 8333

Lucid and concise, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods.

Matrix Analysis for Scientists and Engineers

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Author: Alan J. Laub

Publisher: SIAM

ISBN: 0898715768

Category: Mathematics

Page: 157

View: 9435

"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.

Introduction to Matrix Analysis and Applications

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Author: Fumio Hiai,Dénes Petz

Publisher: Springer Science & Business Media

ISBN: 3319041509

Category: Mathematics

Page: 332

View: 4556

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 and Applied Linear Algebra

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Author: Carl D. Meyer

Publisher: SIAM

ISBN: 0898719518

Category: Mathematics

Page: 718

View: 816

Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer's book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight.

Numerical Matrix Analysis

Linear Systems and Least Squares

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Author: Ilse C. F. Ipsen

Publisher: SIAM

ISBN: 0898716764

Category: Mathematics

Page: 128

View: 8271

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

Matrix Analysis of Structural Dynamics

Applications and Earthquake Engineering

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Author: Franklin Y. Cheng

Publisher: CRC Press

ISBN: 9780203904206

Category: Technology & Engineering

Page: 997

View: 7231

Uses state-of-the-art computer technology to formulate displacement method with matrix algebra. Facilitates analysis of structural dynamics and applications to earthquake engineering and UBC and IBC seismic building codes.

Linear Algebra and Matrix Analysis for Statistics

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Author: Sudipto Banerjee,Anindya Roy

Publisher: CRC Press

ISBN: 1420095382

Category: Mathematics

Page: 580

View: 8928

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 of Electrical Machines

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Author: A. K. Mukhopadhyay

Publisher: New Age International

ISBN: 9788122414455

Category: Electric apparatus and appliances

Page: 264

View: 8714

Electrical Machines May Be Analysed Utilising One Of The Three Methods Viz. Classical Theory, Unified Theory And The Generalised Theory Of Electrical Machines. Generalised Theory May Also Be Regarded As The Matrix Theory Of Electrical Machines Which Requires Only A Knowledge Of The Circuit Equation, Elementary Matrix Algebra And The Principle That The Power Of The System Must Remain Invariant Irrespective Of The Terms In Which It Is Expressed.This Technique Is The Best Approach To Obtain Electrical Machine Performance For Both The Non-Specialist And The Specialist And That The Latter Will Find In It, A Powerful Tool When He Is Faced With More Complicated Performance Problems. An Attempt Has Been Made In This Volume To Study Most Of The Electrical Machines Normally Covered In Undergraduate And Postgraduate Courses Utilising Matrix Analysis. The Book Also Includes Some More Advanced Problems To Indicate The Power And Limitation Of The Method.After An Introduction To The Theory, The Same Methodology Has Been Applied To Static Circuits As Illustrations. Then The Generalised Machines Of First And Second Kinds Have Been Introduced And Analysed Followed By The Different Case Studies. Both Steady State And Transient Analysis Of Conventional Machines Have Been Presented In Both Static And Rotating Reference Frames. The Beauty Of The Matrix Theory Has Been Projected While Developing The Equivalent Circuits Of Different Machines Using Revolving Field Theory Where Physical Concepts Have Been Derived From The Mathematical Models Developed Through Matrix Analysis.The Latest Development Of The Theory Viz. The Development Of State Model Of Different Electrical Machines Has Been Explained Clearly In The Text. These Models May Readily Be Utilised For Stability Analysis Using Computers.The Book Has Been Presented In Such A Way That, It Will Be A Textbook For Undergraduate And Postgraduate Students And Also A Reference Book For The Research Students In The Relevant Area And Practising Engineers.The Treatment Of The Book May Find Wide Application For The Practising Engineers Who Face Day-To-Day Problems In The Practical Field Since The Theory Is Based On Elementary Knowledge Of Matrix Algebra And Circuit Theory Rather Than Complicated Physical Laws And Hypothesis.

Matrix Analysis and Applications

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Author: Xian-Da Zhang

Publisher: Cambridge University Press

ISBN: 1108417418

Category: Mathematics

Page: N.A

View: 8666

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

Applied Linear Algebra and Matrix Analysis

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Author: Thomas S. Shores

Publisher: Springer Science & Business Media

ISBN: 0387489479

Category: Mathematics

Page: 384

View: 9880

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.

Matrix Theory

Basic Results and Techniques

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Author: Fuzhen Zhang

Publisher: Springer Science & Business Media

ISBN: 1461410991

Category: Mathematics

Page: 399

View: 2299

The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields. Major changes in this revised and expanded second edition: -Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms -A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices -A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms.

Matrix Analysis

1925

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Author: Harold Varner McIntosh

Publisher: N.A

ISBN: N.A

Category: Matrices

Page: 430

View: 4945

Matrix Analysis for Statistics

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Author: James R. Schott

Publisher: John Wiley & Sons

ISBN: 1119092469

Category: Mathematics

Page: 552

View: 5572

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.

Matrix Analysis of Structures

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Author: Robert E. Sennett

Publisher: Waveland Press

ISBN: 1478610166

Category: Technology & Engineering

Page: 228

View: 6188

Matrix analysis of structures has become a widely used method in virtually all engineering disciplines. Sennetts outstanding volume, suitable both as a text for students and a reference for professional engineers, clearly presents the displacement method of matrix analysis from its use with a one-dimensional bar element through two-dimensional trusses and frames, finishing with three-dimensional transformations. Special topics, energy methods, and a brief introduction to the finite element method also are included. Computer programming, an essential part of engineering, permeates each chapter to give readers hands-on experience in problem solving.

Computational Matrix Analysis

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Author: Alan J. Laub

Publisher: SIAM

ISBN: 1611972205

Category: Mathematics

Page: 170

View: 7032

This text provides an introduction to numerical linear algebra together with its application to solving problems arising in state-space control and systems theory. The book provides a number of elements designed to help the reader learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis and an introduction to finite (IEEE) arithmetic, alongside discussion of mathematical software topics. In addition to the fundamental concepts, the text covers statistical condition estimation and gives an overview of certain computational problems in control and systems theory. Engineers and scientists will find this text valuable as a theoretical resource to complement their work in algorithms. For graduate students beginning their study, or advanced undergraduates, this text is ideal as a one-semester course in numerical linear algebra and is a natural follow-on to the author's previous book, Matrix Analysis for Scientists and Engineers.

Matrix Analysis Framed Structures

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Author: William Weaver,James M. Gere

Publisher: Springer Science & Business Media

ISBN: 1468474871

Category: Juvenile Nonfiction

Page: 547

View: 646

Matrix analysis of structures is a vital subject to every structural analyst, whether working in aero-astro, civil, or mechanical engineering. It provides a comprehensive approach to the analysis of a wide variety of structural types, and therefore offers a major advantage over traditional metho~ which often differ for each type of structure. The matrix approach also provides an efficient means of describing various steps in the analysis and is easily programmed for digital computers. Use of matrices is natural when performing calculations with a digital computer, because matrices permit large groups of numbers to be manipulated in a simple and effective manner. This book, now in its third edition, was written for both college students and engineers in industry. It serves as a textbook for courses at either the senior or first-year graduate level, and it also provides a permanent reference for practicing engineers. The book explains both the theory and the practical implementation of matrix methods of structural analysis. Emphasis is placed on developing a physical understanding of the theory and the ability to use computer programs for performing structural calculations.