This is the third edition of this well-known introduction to linear algebra. The main changes, apart from the usual improvements during a new edition, are the number of exercises which has more than doubled, new formatting including color printing, new sections on product spaces, quotient spaces, duality, and the chapter on `Operators on Real Vector Spaces' ... . if you ... Read moreliked the previous editions, you will like this new edition even better! (G. Teschl, Monatshefte fur Mathematik, 2016) This third edition, appearing eighteen years after the second edition, is a further polishing of the existing approach. This book was and still is an interesting and useful text for a second course in linear algebra, concentrating on proofs after the concepts and mechanics have been covered in a first course. (Allen Stenger, MAA Reviews, maa.org, May, 2016) AMERICAN MATHEMATICAL MONTHLY The determinant-free proofs are elegant and intuitive. CHOICE Every discipline of higher mathematics evinces the profound importance of linear algebra in some way, either for the power derived from its techniques or the inspiration offered by its concepts. Axler demotes determinants (usually quite a central technique in the finite dimensional setting, though marginal in infinite dimensions) to a minor role. To so consistently do without determinants constitutes a tour de forces in the service of simplicity and clarity; these are also well served by the general precision of Axler's prose. Students with a view towards applied mathematics, analysis, or operator theory will be well served. The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library. ZENTRALBLATT MATH Altogether, the text is a didactic masterpiece. MATHEMATICAL REVIEWS Clarity through examples is emphasized ... the text is ideal for class exercises ... I congratulate the author and the publisher for a well-produced textbook on linear algebra. Show Less