This is a conventional and overpriced introduction to linear algebra that aims for breadth rather than depth. There is more than enough material here for a one-year course, arranged with vectors, matrices, systems of equations, and eigenvalues towards the beginning, and slightly more abstract treatments of orthogonality, spaces, and metrics following. The book touches on an amazing variety of topics, including things rarely seen in introductory texts such as Gerschgorin disks for eigenvalues. Its only conspicuous omission is linear programming. Numerical methods are not addressed explicitly, but most of the background such as Gaussian elimination and *LU*-decomposition is covered. The author says in the Preface (p. x) that “I also believe strongly that linear algebra is essentially about vectors”, and while the book does not literally spend most of its time on vectors, it does make heavy use of geometry and pictures.

The treatment often feels shallow, touching on a subject just long enough for the student to have some familiarity with it. As an example, what is described as a “crash course” in determinants takes 29 pages, and that only covers expansion by minors, Cramer’s rule, and row and column operations. This is a 720-page book, but it is long not because it is wordy but because it has so many examples. My rough estimate is that about 40% of the book is narrative and the other 60% is worked examples and exercises. Overall the exercises are quite good, with the minority being devoted to drill and the majority asking for some kind of reasoning or logical argument. The book includes a number of proofs, both in the body and in the exercises, but does not emphasize proving. The book includes a long list of “applications”, but most of these only sketch very briefly ways that linear algebra can be used, and there’s not enough information to teach you how to apply linear algebra; it’s not a course in applications.

Very Good Feature: specialized indices on the endpapers of notation and of examples, in addition to a thorough conventional index in the back of the book.

The book is supplemented with a long list of ancillary materials, mostly for the instructor, including a companion web site, a solution manual for students, Enhanced WebAssign, a test bank, and an instructor’s guide. I did not examine any of these materials.

So: granted that the book is somewhat bland, what’s *not* to like about it? Certainly the price, at $215 list, is a concern. I might be willing to pay this much for a specialized research monograph that would only sell a few copies and has to make back its fixed costs with a high single-copy price, but it’s ridiculous that a mass-market textbook like this would be so expensive. A good alternative is Strang’s Introduction to Linear Algebra, at less than half the price. It covers the same broad topics, but with more depth and less breadth, and is more application-oriented.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.