Matrix Analysis

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Author: Roger A. Horn,Charles R. Johnson

Publisher: Cambridge University Press

ISBN: 9780521386326

Category: Mathematics

Page: 561

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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.

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: 8818

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: 5389

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.

Introduction to Matrix Analysis

Second Edition

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Author: Richard Bellman

Publisher: SIAM

ISBN: 0898713994

Category: Mathematics

Page: 403

View: 1824

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

Matrix Analysis and Applied Linear Algebra

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Author: Carl D. Meyer

Publisher: SIAM

ISBN: 0898719518

Category: Mathematics

Page: 718

View: 1751

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.

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: 1384

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.

Linear Algebra and Matrix Analysis for Statistics

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Author: Sudipto Banerjee,Anindya Roy

Publisher: CRC Press

ISBN: 1482248247

Category: Mathematics

Page: 580

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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.

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: 5007

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.

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: 8906

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

Matrix Analysis of Structures SI Version

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Author: Aslam Kassimali

Publisher: Cengage Learning

ISBN: 1111426228

Category: Technology & Engineering

Page: 640

View: 2833

This book takes a fresh, student-oriented approach to teaching the material covered in the senior- and first-year graduate-level matrix structural analysis course. Unlike traditional texts for this course that are difficult to read, Kassimali takes special care to provide understandable and exceptionally clear explanations of concepts, step-by-step procedures for analysis, flowcharts, and interesting and modern examples, producing a technically and mathematically accurate presentation of the subject. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Matrix Analysis for Scientists and Engineers

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Author: Alan J. Laub

Publisher: SIAM

ISBN: 9780898717907

Category: Mathematical analysis

Page: 157

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Matrix Analysis for Scientists and Engineers provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra that relieves instructors of the burden of reviewing such material in subsequent courses that depend heavily on the language of matrices. Consequently, the text provides an often-needed bridge between undergraduate-level matrix theory and linear algebra and the level of matrix analysis required for graduate-level study and research. The text is sufficiently compact that the material can be taught comfortably in a one-quarter or one-semester course. Throughout the book, the author emphasizes the concept of matrix factorization to provide a foundation for a later course in numerical linear algebra. The author addresses connections to differential and difference equations as well as to linear system theory and encourages instructors to augment these examples with other applications of their own choosing.

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: 9524

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 Theory

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Author: Joel N. Franklin

Publisher: Courier Corporation

ISBN: 0486136388

Category: Mathematics

Page: 304

View: 7572

Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.

Computational Matrix Analysis

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Author: Alan J. Laub

Publisher: SIAM

ISBN: 1611972205

Category: Mathematics

Page: 170

View: 3641

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 and Applications

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Author: Xian-Da Zhang

Publisher: Cambridge University Press

ISBN: 1108417418

Category: Mathematics

Page: N.A

View: 6169

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

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: 5102

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 of Structures

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Author: Robert E. Sennett

Publisher: Waveland Press

ISBN: 1478610166

Category: Technology & Engineering

Page: 228

View: 7138

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.

Matrix Analysis for Statistics

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Author: James R. Schott

Publisher: John Wiley & Sons

ISBN: 1119092469

Category: Mathematics

Page: 552

View: 4033

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.

Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable

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Author: Edwin Hewitt,Karl Stromberg

Publisher: Springer-Verlag

ISBN: 3662297949

Category: Mathematics

Page: 476

View: 5174