- Paperback: 340 pages
- Publisher: SPRINGER MIHE; 3 edition (18 July 2017)
- Language: English
- ISBN-10: 3319307657
- ISBN-13: 978-3319307657
- Product Dimensions: 15.5 x 2.2 x 23.5 cm
- Boxed-product Weight: 612 g
- Average Customer Review: Be the first to review this item
- Amazon Bestsellers Rank: 24,472 in Books (See Top 100 in Books)
Linear Algebra Done Right 3e Paperback – 18 Jul 2017
Amazon Global Store
Customers who bought this item also bought
Customers who viewed this item also viewed
“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 liked the previous editions, you will like this new edition even better!” (G. Teschl, Monatshefte für 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."
"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."
"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."
From the Back Cover
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.
The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.
No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
No customer reviews
|5 star (0%)|
|4 star (0%)|
|3 star (0%)|
|2 star (0%)|
|1 star (0%)|
Review this product
Most helpful customer reviews on Amazon.com
But the material is mostly theoretically interesting, and does not cover many of the computational tricks in a normal linear algebra class — Gauss-Jordan elimination, a hugely important topic, is not even mentioned. There are so many other things missing, like calculations. You work more with operators and vector spaces than with matrices, and finishing this book won't help you understand the matrix terminology that's common in linear algebra. The book is more suited as a primer to a higher-level theoretical class, like operator theory, functional analysis, or modern algebra. It cannot be a prerequisite to practical/applied courses, like, say, statistics or machine learning. I feel like I've learned a lot after finishing the book, but I don't feel prepared for courses that require a 'working knowledge' of linear algebra.
If you're at all interested in theoretical aspects of algebra or being gently introduced to good proofs, this book will appeal to you. I had never done theoretical math before, and this book was interesting and accessible.
Their education is the responsibility of us all, and how often we forget the old ways...
The proofs are clear but do require the reader to fill in some gaps. This is intended. Open to any page and witness the clarity that so often escape the best efforts of a certain class of instructor; Axler will not suffer any unmotivated concepts. Everything builds from previous definitions until there's just enough structure to flesh out the chapter objectives, thus there's little fat to distract the reader.
Moreover, Axler is so badass that he does away with determinants until the last chapter of the book, he's so pimp he just didn't need any stinking determinants in his proofs. That's right, the last chapter introduces trace and determinants and proceeds to bring everything together into a magnificent mic drop.
I now finally understand why determinants are inextricably tied to notions of volume, and why we must multiply by the Jacobian when performing change of variables in multi-variable integrals, and so on.
A newcomer to linear algebra will get very little of use here, save for the clearest definitions I've ever seen regarding the structure of vector spaces, subspaces and linear operators. For a more applied/introductory approach to linear algebra, one can do much worse than Strang.
I now feel much more comfortable moving onto a graduate-level Linear algebra course after visiting Axler's book, as such, it will be an invaluable reference moving forward.
1. It is for the 2ND CLASS in Linear Algebra. (author says it in preface and back cover)
2. It is a theorem-proof book, and teaches how to think like mathematicians
3. It does NOT cover matrix computations, so that engineers will not get much benefit from it
For the intended audience, it would be one of the best linear algebra books.
It avoids matrix expressions and uses abstract symbols only.
This makes the proofs short and elegant.