Book Description

Written by two top statisticians with experience in teaching matrix methods for applications in statistics, econometrics and related areas, this book provides a comprehensive treatment of the latest techniques in matrix algebra. A well-balanced approach to discussing the mathematical theory and applications to problems in other areas is an attractive feature of the book. It can be used as a textbook in courses on matrix algebra for statisticians, econometricians and mathematicians as well. Some of the new developments of linear models are given in some detail using results of matrix algebra. ... Read more

Book Description

From the reviews: "O'Meara treats his subject from this point of view (of the interaction with algebraic groups). He does not attempt an encyclopedic coverage ...nor does he strive to take the reader to the frontiers of knowledge... . Instead he has given a clear account from first principles and his book is a useful introduction to the modern viewpoint and literature. In fact it presupposes only undergraduate algebra (up to Galois theory inclusive)... The book is lucidly written and can be warmly recommended. J.W.S. Cassels, The Mathematical Gazette, 1965 "Anyone who has heard O'Meara lecture will recognize in every page of this book the crispness and lucidity of the author's style;... The organization and selection of material is superb... deserves high praise as an excellent example of that too-rare type of mathematical exposition combining conciseness with clarity... R. Jacobowitz, Bulletin of the AMS, 1965 ... Read more

Book Description

Undergraduate-level introduction to linear algebra and matrix theory deals with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Also spectral decomposition, Jordan canonical form, solution of the matrix equation AX=XB, and over 375 problems, many with answers.
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Reviews (2)

Linear algebra is fun
So many math books take a relatively simple topic and with the use of horrible notation and confused english, convert it to something esoteric and complicated. This book, however, is anything but that. It involves mathematical rigor, covers a broad range of topics and has answers to selected problems at the back which for a math book, works real well for me. Besides you can't argue with the price.
This book never leaves my desk, recommended strongly.

Supreme intro to advanced linear algebra and matrix analysis
Charles Cullen deserves to pat himself on the back for this one. The first three chapters are the meat of the book which review or, possibly to some, introduce the fundamentals of linear algebra (matrices, vector spaces, and determinants.)

After firmly laying down a foundation from which to work with, Cullen does a remarkable job explaining linear transformations and eigenvalues and eigenvectors (although, some basic calculus is assumed known).

After introducing matrix similarity and Jordan-canonical form, Cullen dabbles in polynomial matrices and more similarity with divisor theorems and polynomial matrix canonical form.

Finally, rounding third plate are an intro into formal matrix analysis (in which some upper-level, although not necessarily advanced, calculus is necessary) and numerical methods. Although these two chapters only encompass about 35 pages total, they do offer a solid foundation for further study.

I recommend this book as it breaks a lot of steps involving matrix calculations down and allows the reader to not only understand how, but why. ... Read more

Book Description

Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.

The algorithms and software at the "leaves" of the decision tree range from the classical QR algorithm, which is most suitable for small dense matrices, to iterative algorithms for very large generalized eigenvalue problems. Algorithms are presented in a unified style as templates, with different levels of detail suitable for readers ranging from beginning students to experts. The authors' comprehensive treatment includes a treasure of further bibliographic information. ... Read more

Book Description

A computer-based course consisting of a complete interactive electronic text combined with a rich set of well chosen real life problems. The easy access to powerful technology allows experimentation. In the lab or lassroom the environment allows a partnership between teacher and student with emphasis on student responsibility. Independent study is also possible.Online tutoring is available. The courseware comes on a CD which contains all of the lessons, some extra tools, and Adobe PDF files for printing selected parts of the lessons: Lessons: Perp Frames and 2D Matrices, Higher Dimensions, Eigensystems, etc. ... Read more

Reviews (1)

Fascinating, unusual approach to matrix theory
Mathematica based tutorial built largely around Singular Value Decomposition analysis. Gives a very solid intuitive understanding of the subject. ... Read more

Book Description

Concise undergraduate text focuses on problem solving, rather than elaborate proofs. The first three chapters present the basics of matrices, including addition, multiplication, and division. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. He also looks into special matrices—including complex numbers, quaternion matrices, and matrices with complex entries—transpose matrices; the trace of a matrix; the cross product of matrices; eigenvalues and eigenvectors; and infinite series of matrices. Exercises at the end of each section give students further practice. Prerequisites include algebra and (in the later chapters) solid geometry. 1961 edition. 20 black-and-white illustrations.
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Reviews (1)

Buyer Beware Mistakes & lack of Exercise Solutions
Just a quick review to warn people like me who buy books like these to help us in our autodidact pursuits. I bought this Dover book because I trusted Dover publications and am now disappointed to say that this trust is now in question. The book has some merit: the flow and examples are clear and well laid out however, THERE ARE NO SOLUTIONS TO THE EXERCISES!
Be aware that there are some glaring mistakes even to the beginner's eyes. For example, the author says "We may determine a 4X4 matrix..." and then represents this 4x4 with a 5x5 matrix. And he contradicts a commutivity theorem by saying that where two matrices A and zero share the same nxn row & column dimensions An+0n=A and then right after this he says A+0=0 on pp. 12-13. This is wrong! How am I supposed to trust further examples from this book? Sorry, I'll have to permanently shelve it...
Good luck.
IndiAndy
Aspiring Autodidact ... Read more

Book Description

The field of generalized inverses has grown much since the appearance of the first edition in 1974, and is still growing. This book accounts for these developments while maintaining the informal and leisurely style of the first edition.New material has been added, including a chapter on applications, an appendix on the work of E.H. Moore, new exercises and applications. ... Read more

Reviews (1)

An excellent book
This book is well-written and the authors explain the relationship among generalized inverses very clearly, unlike some other books. ... Read more

Book Description

This book is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. Stressing depth over breadth, Professor Stewart treats the derivation and implementation of the more important algorithms in detail. The notes and references sections contain pointers to other methods along with historical comments.

The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method.

The volumes in this survey are not intended to be encyclopedic. By treating carefully selected topics in depth, each volume gives the reader the theoretical and practical background to read the research literature and implement or modify new algorithms. The algorithms treated are illustrated by pseudocode that has been tested in MATLAB implementations.

Audience

The volumes in the series are intermediate-level monographs, suitable for self-study by professionals and graduate students in the sciences and engineering. The first volume, Matrix Algorithms, Volume I: Basic Decompositions, was published by SIAM in 1998 (ISBN 0-89871-414-1). ... Read more

Book Description

Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.
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Reviews (2)

Excellent
I have just read part I of the book (table of contents below), and I like it very much. So many information, on so few pages. Everything is threated in FULL generality, and proves are included for the main theorems. This book has also an excellent encyclopedia function, as it contains the main properties of anything that one can think of.

Beware: I have some mathematical background, and if you fully want to appreciate this book you will need this. (don't buy this book if this would be your first confrontation with matrices).

Table of contents:

I Survey of matrix theory
1 Introductory concepts
2 Numbers associated with matrices
3 Linear equations and canonical forms
4 Special classes of matrices, commutativity
5 Congruence

II Convexity and matrices
1 Convex sets
2 Convex functions
3 Classical Inequalities
4 Convex functions and matrix inequalities.
5 Nonnegative matrices

III Localization of characteristic roots
1 Bounds for characteristic roots
2 Regions containing characteristic roots of a general matrix
3 Characterstic roots of a general matrix
4 The spread of a matrix
5 The field of values of a matrix

A classic compilation of results in this field.
This book is not really a review of matrix theory; the focus is on inequalities, mainly for PD matrices, convex functions and eigenvalue problems. The book tries to present a general framework, a-la Hardy, but is not quite as successful. Nevertheless, if you need to find that elusive inequality that you saw in undergraduate, this book will likely contain it. This book should be on every mathematical researcher's shelf. ... Read more

Book Description

This is the most extensively visual book in the market—highlighted by hundreds of Mathematica and MATLAB generated figures throughout. It now contains a full chapter of material on matrices and eigenvalues up front. All of Multivariable Calculus has been rewritten with matrix notation.Chapter topics include infinite series, vectors and matrices, curves and surfaces in space, partial differentiation, multiple integrals, and vector calculus. ... Read more

Book Description

Solid, mathematically rigorous introduction covers diagonalizations and triangularizations of Hermitian and non-Hermitian matices, the matrix theorem of Jordan, variational principles and perturbation theory of matrices, matrix numerical analysis, in-depth analysis of linear computations, more. Only elementary algebra and calculus. Problem-solving exercises. 1968 ed.
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Reviews (2)

A True Classic
I have been using this book for many years as a reference and as a source of interesting diversions. Bellman's typically dense style and leaving some proofs to the reader makes for a lot more material than its 387 pages would indicate. The main topics begin with matrix theory in maxima and minima and quickly get to dynamic programming, differential equations, and stability theory. This is the one good reference I have found on Markov matrices (not Markov processes). The last few topics are control processes, invariant imbedding, and Tychonov regularization. Side topics include Vandermonde matrices, Gaussian quadrature, and much, much more.

Big name - big bomb
I had to use this book as a text for a class on Matrix Theory. It is really hard to learn much about matrices from this book. It is poorly organized and assumes you already know a lot. Two quarters of graduate level linear algebra was not enough. I actually drew on results from a number of different graduate courses (diffential equations, real analysis, etc.) to help me and still found this book difficult to learn from.

Many of the sections of the book present key material in a very general way. The proofs are often very condensed and sometimes use more advanced results that can only be found with outside research. Many of the problems are very difficult and require advanced techniques not presented in the book.

Two positives - it has an extensive bibliography and could be a good source of challenging problems for the more advanced student. ... Read more

Book Description

As a basis of equation and problem-solving, linear algebra is the most widely taught sub-division of pure mathematics. Building on both skills and knowledge attained during A-level and earlier degree modules in linear algebra, "Matrices and Quadratic Forms" provides a lively and accessible introduction to matrices and quadratic forms. Examples and exercises are used as teaching aids throughout and ideas for investigation and project work help to place the subject in context. Student motivation and learning is encouraged by the inclusion of historical contexts, real-life situations and the discussion of links with other areas of mathematics. Providing a concise and thorough introduction to matrices and quadratic forms, this is an essential purchase for all students of mathematics.

Ideal second text in linear algebra, this book follows on from Allenby's Linear Algebra.
Concise and affordable.
Written in a straightforward and accessible style by an authority in the field. ... Read more

Book Description

Part of the Duxbury Classic series, Franklin A. Graybills MATRICES WITH APPLICATIONS TO STATISTICS focuses primarily on matrices as they relate to areas of multivariate analysis and the linear model. This seminal work is a time tested, authoritative resource for both students and researchers. ... Read more

Book Description

This book is the first to pay special attention to the combined issues of speed and numerical reliability in algorithm development. These two requirements have often been regarded as competitive, so much so that the design of fast and numerically reliable algorithms for large-scale structured systems of linear equations, in many cases, remains a significant open issue. Fast Reliable Algorithms for Matrices with Structure helps bridge this gap by providing the reader with recent contributions written by leading experts in the field.

The authors deal with both the theory and the practice of fast numerical algorithms for large-scale structured linear systems. Each chapter covers in detail different aspects of the most recent trends in the theory of fast algorithms, with emphasis on implementation and application issues. Both direct and iterative methods are covered.

This book is not merely a collection of articles. The editors have gone to considerable lengths to blend the individual papers into a consistent presentation. Each chapter exposes the reader to some of the most recent research while providing enough background material to put the work into proper context. ... Read more

Book Description

This text covers several aspects and solutions of the problems of linear vibrating systems with a finite number of degrees of freedom. It offers a detailed account of the part of the theory of matrices necessary for efficient problem-solving, beginning with the first four chapters' focus on developing the necesary tools in matrix theory. The following chapters present numerical procedures for the relevant matrix formulations and the relevant theory of differential equations. The book is directed toward a wide audience of applied mathematicans, scientists, and engineers who are interested in these problems from either practical or theoretical points of view. Although mathematically sound, the treatment involves readers in a minimum of mathematical abstraction. A familiarity and facility with matrix theory is assumed, along with a knowlege of elementary calculus, including the rudiments of the theory of functions of a complex variable. Unabridged republication of the edition published by Pergamon Press, Oxford, 1966. Preface. Bibliographical Notes. References. Index.
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Reviews (1)

concise treatment of matrices
This book gives a very concise treatment fo matrix algebra, covering from first principles the basic mathematics. It is oriented toward statistical applications such as the least squares solution in regression, concepts of principal components and other multivariate statistical topics where matrices play an important role. I particularly like the way determinants were introduced and motived by the generalization of "never divide by zero." It is a good reference for statistical practitioners including statisticians, engineers, biologists and social scientists. For those interested in a more thorough treatment there are other noteworthy books, one by Searle and one by Graybill. Healy's text is inexpensive and easy to use as a reference particularly the paperback edition that I have. ... Read more

Book Description

The Matrix version combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities.This book contains an entire chapter on calculus of transcendental functions, a new chapter on matrices and eigenvalues, and increased coverage of differential equations.For professionals who need to brush up on their calculus skills. ... Read more