- Series: Undergraduate Texts in Mathematics
- Paperback: 251 pages
- Publisher: Springer; 2nd edition (June 2, 2010)
- Language: English
- ISBN-10: 0387982582
- ISBN-13: 978-0387982588
- Product Dimensions: 7.5 x 0.6 x 9.2 inches
- Shipping Weight: 1.2 pounds
- Average Customer Review: 3.9 out of 5 stars See all reviews (102 customer reviews)
- Amazon Best Sellers Rank: #81,832 in Books (See Top 100 in Books)
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Linear Algebra Done Right (Undergraduate Texts in Mathematics) 2nd Edition
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From the reviews:
"This second edition of an almost determinant-free, none the less remarkably far-reaching and didactically masterly undergraduate text on linear algebra has undergone some substantial improvements. First of all, the sections on selfadjoint operators, normal operators, and the spectral theorem have been rewritten, methodically rearranged, and thus evidently simplified. Secondly, the section on orthogonal projections on inner-product spaces has been extended by taking up the application to minimization problems in geometry and analysis. Furthermore, several proofs have been simplified, and incidentally made more general and elegant (e.g., the proof of the trigonalizability of operators on finite-dimensional complex vector spaces, or the proof of the existence of a Jordan normal form for a nilpotent operator). Finally, apart from many other minor improvements and corrections throughout the entire text, several new examples and new exercises have been worked in. However, no mitigation has been granted to determinants. Altogether, with the present second edition of his text, the author has succeeded to make this an even better book."
AMERICAN MATHEMATICAL MONTHLY
"The determinant-free proofs are elegant and intuitive."
"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."
"Altogether, the text is a didactic masterpiece."
From the reviews of the second edition:
Linear Algebra Done Right
"The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library."—CHOICE
"A didactic masterpiece."—ZENTRALBLATT MATH
“This book can be thought of as a very pure-math version of linear algebra … . it focuses on linear operators, primarily in finite-dimensional spaces … . Axler has come up with some very slick proofs of things that … makes the book interesting for mathematicians. The book is also very clearly written and fairly leisurely. … Axler concentrates on the properties of linear operators, and doesn’t introduce other concepts unless they’re really necessary.” (Allen Stenger, The Mathematical Association of America, December, 2010)
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Top Customer Reviews
I got this book for a class, and read the second half of the book because I liked it that much. The chapters are fairly short (maybe 10-30 pgs) but instructive. There are about 30 questions at the end of each chapter. The author does a good job of explaining things.
I would recommend this book for anyone who wants a different perspective that isn't immediately applied. This book isn't a "how to use linear algebra to solve your computational problems" book but rather a "mathematical underpinnings of linear algebra through proofs using vector spaces" book. With that said, the proofs aren't super complicated. If you feel you can use linear algebra but don't really *understand* it, then this is definitely a book to consider.
I used this textbook to "replace" the textbook required for my undergraduate Applied Linear Algebra Course. My original "Applied" textbook skipped over necessary abstractions and concepts which I required to actually apply the methodologies effectively.
This text is phenomenal. Not only did it assist me in my applied coursework and functionally replace a much longer and less clear text- but it gave me the motivation to pursue the subject further.
1. Excellent for linear algebra beginners.
2. Excellent clarification of abstract algebraic concepts.
3. Great preparation for abstract mathematics.
4. Excellent exercises.
1. No solutions to exercises.
While it is targetted at the upper undergraduate level of mathematical maturity, I found that it's clear exposition and development of the topics (and the fact that it provides an alternative approach with clear explanations) was useful even in an upper graduate course as a suppliment to the main text. I think it would also do very well as the primary text for an introductory course or for self-study by anyone with reasonable previous exposure to mathematical proofs.