A (terse) introduction to linear algebra /

In this delightful little (terse) book, authors Yitzhak Katznelson (Stanford Univ.) and Yonatan Katznelson (Univ. of California, Santa Cruz) focus "on the principal ideas and results of linear algebra qua linear algebra." The self-contained, well-written work assumes mathematical maturity and the ability to deal with abstract and formal reasoning. It covers vector spaces, linear operators and matrices, inner product spaces and structure theorems (Jordan canonical form), and a few additional topics. To suggest the level of the book, vector spaces are presented over arbitrary fields, but the examples only require knowledge of real and complex numbers. Perhaps more indicative is the development of the determinant via nontrivial alternating n-forms on an n-dimensional vector space, all of which is fully developed. The proofs are quite sufficient although intentionally brief, leaving the details for the reader. There is a short list of exercises at the end of the sections. It is a concise, thorough introduction to linear algebra. There are no applications, but anyone teaching with this book should be able to provide them with little difficulty. Summing Up: Recommended. Upper-division undergraduate through professional collections. J. R. Burke Gonzaga University