Summary

An accessible introduction to the theoretical and computational aspects of linear algebra using MapleTM

Many topics in linear algebra can be computationally intensive, and software programs often serve as important tools for understanding challenging concepts and visualizing the geometric aspects of the subject. Principles of Linear Algebra with Maple uniquely addresses the quickly growing intersection between subject theory and numerical computation, providing all of the commands required to solve complex and computationally challenging linear algebra problems using Maple. The authors supply an informal, accessible, and easy-to-follow treatment of key topics often found in a first course in linear algebra.

Requiring no prior knowledge of the software, the book begins with an introduction to the commands and programming guidelines for working with Maple. Next, the book explores linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics such as vectors, dot product, cross product, and vector projection are explained, as well as the more advanced topics of rotations in space, rolling a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear transformations from Rn to Rm, the geometry of linear and affine transformations, least squares fits and pseudoinverses, and eigenvalues and eigenvectors.

The authors explore several topics that are not often found in introductory linear algebra books, including sensitivity to error and the effects of linear and affine maps on the geometry of objects. The Maple software highlights the topic's visual nature, as the book is complete with numerous graphics in two and three dimensions, animations, symbolic manipulations, numerical computations, and programming. In addition, a related Web site features supplemental material, including Maple code for each chapter's problems, solutions, and color versions of the book's figures.

Extensively class-tested to ensure an accessible presentation, Principles of Linear Algebra with Maple is an excellent book for courses on linear algebra at the undergraduate level. It is also an ideal reference for students and professionals who would like to gain a further understanding of the use of Maple to solve linear algebra problems.

Choice Review

This is a textbook for a very computation-oriented course on linear algebra. The topics that are covered are not overly different from most competing course resources: matrixes and matrix operations, linear transformations over real vector spaces, determinants, affine spaces, eigenvectors, and eigenvalues. Shiskowski (Eastern Michigan Univ.) and Frinkle (Southeastern Oklahoma State Univ.) do include a few topics that are less frequently addressed in other books, such as rotations in space or sensitivity to error. However, the Maple software package takes a central role here, sometimes at the expense of important, beautiful, and entertaining mathematical results. For instance, the product theorem of determinants, a striking and fundamental result, is not stated in its full generality, and even its special cases are relegated to the exercises. The authors do not present applications of matrix multiplication to discrete mathematics (adjacency matrices of graphs), and only give a recursive definition of determinants. Including some of these gems would have made the book more enjoyable for both students and instructors. Summing Up: Optional. Upper-division undergraduates. M. Bona University of Florida