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.
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.
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this 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. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.
"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.
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.
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.
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.
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.