Book Description

Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stresses insight, understanding, and applications. Among its most outstanding features is the integration of MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations in that section and offers code for the graphics and some algorithms used in the text.All of the material is presented from a matrix point of view with enough rigor for students to learn to compose arguments and proofs and adjust the material to cover other problems. The treatment includes optional subsections covering applications, and the final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphics, and topology.Filled with illustrations, examples, and exercises that reinforce understanding, Matrix Theory and Applications with MATLAB allows readers to experiment and visualize results in a way that no other text does. Its rigor, use of MATLAB, and focus on applications better prepares them to use the material in their future work and research, to extend the material, and perhaps obtain new results of their own. ... Read more

Reviews (1)

Thorough, Well-Written Introduction to Matrices
I highly recommend this Dover text as either a self-tutorial or as a quick review of matrices. I initially thought that a text for the "non-mathematics science student" might prove too elementary to be useful. It actually provides a thorough, concise (but not terse) introduction to matrices that is quite appropriate for undergraduate students in physics or chemistry. The sections on eigenvalues and eigenvectors, on diagonalization of matrices, and on functions of matrices were particularly good.

I am reasonably familiar with linear algebra and matrices and read this book partially for review, but more out of general interest. I was surprised at how effectively Stephenson managed in only 150 pages to explore key topics at some depth without sacrificing his tutorial style. I am puzzled that that this book is not better known. It is quite well-written and I give it five stars. The price is quite affordable and I don't believe that you will find a better overview of matrices at even much higher prices.

Don't be concerned that this is not a new book (first published in 1965). The matrix notation is modern and consistent with current textbooks. The author, G. Stephenson, was Emeritus Reader of Mathematics, Imperial College of Science and Technology, University of London.

I also recommend two other Dover reprints. Matrices and Transformations by Anthony Pettofrezzo is a more basic introduction. An Introduction to Linear Algebra and Tensors by M. A. Akivis and V. V. Goldberg is a good next step after Stephenson's text. ... Read more

Book Description

In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields. ... Read more

Book Description

This book is a comprehensive survey of matrix perturbation theory, a topic of interest to numerical analysts, statisticians, physical scientists, and engineers. In particular, the authors cover perturbation theory of linear systems and least square problems, the eignevalue problem, and the generalized eignevalue problem as wellas a complete treatment of vector and matrix norms, including the theory of unitary invariant norms. ... Read more

Book Description

This revision of a well-known text includes more sophisticated mathematical material. A new section on applications provides an introduction to the modern treatment of calculus of several variables, and the concept of duality receives expanded coverage. Notations have been changed to correspond to more current usage. ... Read more

Reviews (1)

Excellent text on matrix solution algorithms.
Excellent text focusing on solution of matrix equations. It surpases other books in this category by including many of the common practical pitfalls in writing program code for solving matrix equations. The text and code fragments are well written and clearly discussed. Code optimization is considered with discussions on such topics as memory core use and specialized matrix considerations that haunt the practicing programmer on a daily basis. This book deserves a spot on every engineer's bookshelf. ... Read more

Book Description

Matrices for Engineers is designed to supply engineers and engineering students with a foundation in matrix theory and versatility in the manipulation of matrices. The book's approach provides the necessary material in a direct manner, with examples that illustrate each concept as it appears. The book emphasizes methodology and includes topics such as how to obtain the characteristic polynomial of a matrix; the factorizations of a coefficient matrix for ease of computation; and linear transformations from an intuitive and engineering point of view, in which conditions at one point in a system induce conditions at another. Indeed, it covers computational techniques and goes beyond matrix algebra to include matrix calculus. Perfect for self-study, Matrices for Engineers also functions as a supplement to Oxford University Press's popular Linear Circuit Analysis, Second Edition (ISBN 0-19-513666-7), by Raymond A. DeCarlo and Pen-Min Lin or any introductory electrical engineering text, such as Introduction to Electrical Engineering (ISBN 0-19-513604-7) by Mulukutla S. Sarma. It can also be used to help in preparing for the Fundamentals of Engineering (FE)/Engineer-in-Training (EIT) exam and the Professional Engineer (PE) exam.Also Available from Oxford University Press DeCarlo and Lin's Linear Circuit Analysis, Second Edition (ISBN 0-19-513666-7): Allan's Circuits Problems by Allan D. Kraus (ISBN 0-19-514248-9) Ray's Linear Circuits Lectures to Accompany Linear Circuit Analysis, Second Edition, by Raymond A. DeCarlo and Pen-Min Lin (ISBN 0-19-514751-0) Solutions Manual to Accompany Linear Circuit Analysis, Second Edition, by Raymond A. DeCarlo and Pen-Min Lin (ISBN 0-19-514218-7) Microsoft PowerPoint Overheads to Accompany Linear Circuit Analysis, Second Edition (ISBN 0-19-514724-3) Sarma's Introduction to Electrical Engineering (ISBN 0-19-513604-7): Solutions Manual to Accompany Introduction to Electrical Engineering by Mulukutla S. Sarma (ISBN 0-19-514260-8) Microsoft PowerPoint Overheads to Accompany Introduction to Electrical Engineering (ISBN 0-19-514472-4) KC's Problems and Solutions to Accompany Microelectronic Circuits, Fourth Edition, by K. C. Smith (ISBN 0-19-511771-9) Spice, Second Edition, by Gordon Roberts and Adel Sedra (ISBN 0-19-510842-6) Getting Started with MATLAB: A Quick Introduction for Scientists and Engineers (Version 6), by Rudra Pratap (ISBN 0-19-515014-7) ... Read more

Book Description

Random matrices arise from, and have important applications to, number theory, probability, combinatorics, representation theory, quantum mechanics, solid state physics, quantum field theory, quantum gravity, and many other areas of physics and mathematics. This volume of surveys and research results, based largely on lectures given at the Spring 1999 MSRI program of the same name, covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems. Its focus on the interaction between physics and mathematics will make it a welcome addition to the shelves of graduate students and researchers in both fields, as will its expository emphasis. ... Read more

Book Description

This book was written by experienced practitioners for an increasingly popular course. It includes actual examination questions giving students plenty of practice to help develop exam technique. It also includes ICT activities for full support in developing statistics in this media. This book is fully differentiated to provide for all course and coursework requirements for Foundation and Higher Tiers. Review sections in every chapter are ideal for revision and consolidation of learning. ... Read more

Book Description

This book provides a systematic and uniform presentation of elimination methods and the underlying theories, along the central line of decomposing arbitrary systems of polynomials into triangular systems of various kinds. Highlighting methods based on triangular sets, the book also covers the theory and techniques of resultants and Gröbner bases. The methods and their efficiency are illustrated by fully worked out examples and their applications to selected problems such as from polynomial ideal theory, automated theorem proving in geometry and the qualitative study of differential equations. The reader will find the formally described algorithms ready for immediate implementation and applicable to many other problems. Suitable as a graduate text, this book offers an indispensable reference for everyone interested in mathematical computation, computer algebra (software), and systems of algebraic equations. ... Read more

Book Description

Simple exposition of linear programming and matrix games covers convex sets in the Cartesian plane and the fundamental extreme point theorem for convex polygons; the simplex method in linear programming; the fundamental duality theorem and its corollary, von Neumann’s minimax theorem; more. Easily understood problems and illustrative exercises. 1963 edition.
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Book Description

The first chapter of this book provides a brief treatment of the basics of the subject. The other chapters deal with the various decompositions of non-negative matrices, Birkhoff type theorems, the study of the powers of non-negative matrices, applications of matrix methods to other combinatorial problems, and applications of combinatorial methods to matrix problems and linear algebra problems.

The coverage of prerequisites has been kept to a minimum. Nevertheless, the book is basically self-contained (an Appendix provides the necessary background in linear algebra, graph theory and combinatorics). There are many exercises, all of which are accompanied by sketched solutions.Audience: The book is suitable for a graduate course as well as being an excellent reference and a valuable resource for mathematicians working in the area of combinatorial matrix theory. ... Read more

Book Description

In this book the author describes his own technique of constructing Green's functions and matrices for the elastostatic Lame's equations and provides examples of applications in applied mathematical physics.

Designed for graduate and postgraduate students investigating such areas as elasticity, thermoelasticity, mechanics, heat conduction, electro- and magneto conduction, electronics, radio-physics, hydrodynamics,and conduction of moisture, the text will also be of interest to engineers and researchers working in these fields.

Many problems and solutions are included while an accompanying CD-ROM features examples and applications of Green's functions for Poisson's equation, and 2D and 3D Green's matrices for Lame's equations.

Contents:Preface;Introduction;PART I - THE BASIS OF INCOMPRESSIBLE INFLUENCE ELEMENTS METHOD:Integral Representations of Solutions in the Theory of Elasticity;Constructive Solutions for Green's Matrices in the Form of Integrals.PART II - HANDBOOK OF GREEN'S FUNCTIONS AND MATRICES:Green's Functions and Matrices for Two-Dimensional Domains;Green's Functions and Matrices for Three-Dimensional Domains.Notations;References;Index. ... Read more

Book Description

The symplectic eigenvalue problem is helpful, e.g., in analyzing a number of different questions that arise in linear control theory for discrete-time systems. Industrial production and technological processes may suffer from unwanted behavior, e.g., losses in the start-up and change-over phases of operation, pollution, emission of harmful elements, and production of unwanted by-products. Control techniques offer the possibility of analyzing such processes in order to detect the underlying causes of the unwanted behavior. This monograph describes up-to-date techniques for solving small to medium-sized as well as large and sparse symplectic eigenvalue problems. The text presents all developed algorithms in Matlab-programming style and numerical examples to demonstrate their abilities, all of which makes the text accessible to graduate students in applied mathematics and control engineering, as well as to researchers in these areas. ... Read more

Book Description

A real matrix is positive semidefinite if it can be decomposed as A=BB¢. In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A=BB¢ is known as the cp-rank of A.

This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp-rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined. ... Read more

Book Description

A complete study on an important class of linear dynamical systems–positive linear systems

One of the most often-encountered systems in nearly all areas of science and technology, positive linear systems is a specific but remarkable and fascinating class. Renowned scientists Lorenzo Farina and Sergio Rinaldi introduce readers to the world of positive linear systems in their rigorous but highly accessible book, rich in applications, examples, and figures.

This professional reference is divided into three main parts: The first part contains the definitions and basic properties of positive linear systems. The second part, following the theoretical exposition, reports the main conceptual results, considering applicable examples taken from a number of widely used models. The third part is devoted to the study of some classes of positive linear systems of particular relevance in applications (such as the Leontief model, the Leslie model, the Markov chains, the compartmental systems, and the queueing systems). Readers familiar with linear algebra and linear systems theory will appreciate the way arguments are treated and presented.

Extraordinarily comprehensive, Positive Linear Systems features:

• Applications from a variety of backgrounds including modeling, control engineering, computer science, demography, economics, bioengineering, chemistry, and ecology
• References and annotated bibliographies throughout the book
• Two appendices concerning linear algebra and linear systems theory for readers unfamiliar with the mathematics used

Farina and Rinaldi make no effort to hide their enthusiasm for the topics presented, making Positive Linear Systems: Theory and Applications an indispensable resource for researchers and professionals in a broad range of fields. ... Read more