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Applied Linear Algebra and Matrix Analysis

Thomas S. Shores
Springer Verlag
Publication Date: 
Number of Pages: 
Undergraduate Texts in Mathematics
[Reviewed by
Henry Ricardo
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This book is intended for a one or two semester course, with emphasis on linear algebra as an experimental science. Matrix analysis and mathematical modeling are emphasized. There is a nice blend of theory, computation, and application. Each chapter ends with a starred (optional) section titled Computational Notes and Projects. This material is independent of specific hardware and software platforms, and the author’s website supplies downloadable files containing text-specific Maple and Mathematica notebooks, as well as MATLAB Files Program files and errata sheets. There is a thirteen-item bibliography at the end of the book.

The text is written in a nice conversational style. Proofs are provided for most results; but in those cases where a full proof is not given, there is often an illuminating example or heuristic argument. Key definitions and theorems are highlighted by titles in the margins. The rich assortment of applications scattered among the examples and projects includes discussions of Markov chains, input-output models, difference equations, graph theory, computer graphics, and discrete dynamical systems.

In providing reader tasks, the author distinguishes between exercises, which test basic skills and have odd-numbered answers in the back, and problems, which are more advanced conceptually or computationally. No answers are provided for problems, only hints given for those marked with an asterisk. A complete solutions manual is available to adopters.

The author also provides many computer exercises, projects, and report topics (requiring the equivalent of “scientific term papers”). The projects and reports are meant to encourage cooperative learning, with students working in teams. Instructors wanting to encourage precision in mathematical writing will find these assignments helpful.

The material had been available online for about ten years and has benefited from many readers’ comments and suggestions. This is a good text for those who want to introduce their students to applied discrete mathematics and challenge them individually and in groups to experiment and push beyond the standard topics.

Henry Ricardo ( is Professor of Mathematics at Medgar Evers College of The City University of New York and Secretary of the Metropolitan NY Section of the MAA. His book, A Modern Introduction to Differential Equations, was published by Houghton Mifflin in January, 2002; and he is currently writing a linear algebra text.

 Preface.- Linear Systems of Equations.- Matrix Algebra.- Vector Spaces.- Geometrical Aspects of Standard Spaces.- The Eigenvalue Problem.- Geometrical Aspects of Abstract Spaces.- Table of Symbols.- Answers to Selected Exercises.- References.- Index.