Linear Algebra Done Right

Not only is Axler's approach sound, but his writing is very lucid and clear as well. You will never leave a proof feeling unsatisfied or confused; it almost reads like a book. I wish all math books were written this way.

My only gripe with the book is the lack of solutions to the problems. Those who use the book for self-study will feel particular frustrated in this regard. I hope some effort is taken to assuage this problem in future editions. Also, more material on linear functionals and multilinear mappings (tensors) would be nice.

In summary, this is an outstanding book; I highly recommend it.


Minimalist: very easy to read, but limited in the material it covers   August 27, 2005
Alexander C. Zorach (New Haven, CT)
14 out of 15 found this review helpful

This book is very easy to read, especially compared to other books on abstract linear algebra. The proofs are easy to follow and give intuitive insight into the results. Most importantly, this book makes linear algebra fun, unlike most of the typical introductory undergrad texts.

The largest weakness of this book is that it does not cover much material. It covers the basics of vector spaces, defines and proves a few basic theorems about eigenvectors and eigenvalues, and then ends. A lot of the discussion in the more advanced chapters (the chapter on inner products comes to mind) is inadequate for anyone who intends to actually use the material. The discussion of determinants is an afterthought, and the book doesn't even touch bilinear forms, doesn't explore geometry very much, nor does it really provide any glimpse into any of the vast applications of linear algebra that are out there.

This book is minimalist; it is excellent in that respect, but it is not even close to comprehensive. I think that if you use this book for a class, it should be supplemented by one or more other books. This book would be excellent for self-study because it is so clear, but it is not very useful as a reference; 90% of the time I try to look something up in this book, I find it's simply not there. I find that this book can be complemented very well by Shilov's book (which starts from determinants, something this book does not focus on).


Elegant theoretical presentation of linear algebra   June 2, 2004
Charles R. Williams (Akron, OH United States)
11 out of 11 found this review helpful

This is a short, elegant presentation of linear algebra appropriate for upper level undergraduate math majors with a theoretical bent. The student has perhaps taken a linear algebra course designed for engineers and scientists. Such a student is comfortable reading mathematics and writing proofs. It is meant to be read and re-read until the ideas are absorbed. The exercises are relatively easy and no answers are provided. With exercises of this sort you generally know if you are on the right track and they require you to understand the presentation in the text and process the ideas in a straight forward way.

Of course, there is nothing in this book about applications or the computational aspects of applying linear algebra.

The price is right. This could be a very useful purchase even if it's not assigned as a text.


Great Book   October 13, 2001
Joseph Borrego (Leverett, MA United States)
10 out of 12 found this review helpful

This is an example of an extremely elegant book that does lose sight of the real world (Euclidean Spaces). For an undergraduate math major is one of the best books that I have ever seen. I really would love to teach a course from it. The book does not meet all needs. This is the beauty of the book, it written for people wishing to learn the basics of Linear Algebra from a mathematical point of view and it does it wonderfully. Most books, these days, try to do so much that they end up doing nothing. This book is not suitable for a first course in Linear Algebra. It rather important that the reader have some prior knowlege in order to fully appreciate some of the abstractions. Many second Linear Algebra courses try to concentrate on applications. This book is not good for this purpose. The book does provide a wonderful foundation to build the applications later. I am in complete agreement with the author's contention that it better to look at Linear Transformations than matrices. However, my teaching experience tells that before one does this one should look at the properties of matrices first and then translate the properties in terms of Linear Transformations.


Very good   November 15, 2003
Toan Vu Phan (Northwestern U, IL USA)
6 out of 9 found this review helpful

An well written book with an elegant approach to linear algebra, by a famous author.
The book has good exercises, thou not very hard. I only wish Prof Axler had talked a little bit more about applied linear algebra.