Mathematics education is one of the many fields the computer has had an impact on, and this book is an example of the resulting change. Not very long ago, an introductory book about linear algebra, even with an emphasis on applied mathematics rather than on pure mathematics, would simply not have had such a large number of computer-generated figures, a PostScript tutorial, exercises that use PostScript, or, sprinkled throughout the text, comments and warnings about computations carried out on the computer.

Many liberal arts students will like this book; many instructors may also have a favorable first impression of it. I have already mentioned the computer-generated figures that help in the visualization and comprehension of the underlying material. Also helping this process are many examples and hand-drawn sketches, although the font used in the sketches makes many of them difficult to read. Many examples have an accompanying figure or sketch. The tone of the text is notable for its accessible style and comprehensive explanations that pay particular attention to applications students can relate to. In this respect, however, the authors err in a perhaps unintended way: in an effort to avoid becoming too dry, they forgo careful definitions and mathematical rigor in exchange for motivation, examples, graphics, and an abundant, annoying use of quotation marks (mostly improperly used) and exclamation points. As a result, if a student wants to review the meaning of a concept or !term, in lieu of a definition, he may have to search the index and do a fair amount of reading, or consult a glossary that may be incomplete or at times unclear.

The authors intend the book to be an introduction to linear algebra for engineers or computer scientists in preparation for further work in computer graphics or geometric modeling. I would not recommend using this book as a textbook in a mathematics curriculum. I believe that computer scientists deserve the opportunity to develop patterns of thought and work that lead to the development of mathematical intuition and not merely to algorithmic and computational expertise. I question the belief that a chatty, but unfocused presentation--the authors use the phrase “intuitive, geometric manner”--leads students to a deeper level of understanding than does a classical approach that carefully builds up precise definitions and rigorous proofs.

The book has more than enough material for a one-semester course in linear algebra. In addition to the preface, the book contains 18 chapters, a brief PostScript tutorial, solutions to selected problems, a bibliography, and an index. Chapters 1 through 7 cover points, vectors, lines, linear maps, linear systems, affine maps, eigenvalues, and eigenvectors in two-dimensional spaces. Triangles and conics are addressed in chapters 8 and 9. The topics addressed in chapters 1 through 7 are revisited, in three-dimensional spaces, in chapters 10 through 13. Chapters 14 through 16 cover material in higher dimensions. Included here are Gauss elimination, LU decomposition, Householder’s and iterative methods, determinants, inverse matrices, linear spaces, linear products, and the Gram-Schmidt process. Chapter 17 covers polylines and polygons, and chapter 18 deals with the generation of curves. Most chapters end with a summary of important topics.

The book’s accompanying Web site is well done: an errata section gives, in addition to each correction, the name of the person who found the mistake and the date the correction was posted. Available downloads include several PDF files, some of which expand the material in the book. All of the book’s figures can be downloaded as PostScript and JPEG files; all hand-drawn sketches can also be downloaded as JPEG files. Instructors can request solutions to all exercises, sample exams with solutions, and other material. I did find it difficult to match the downloaded figures and sketches to corresponding figures and sketches in the book.