This best-selling textbook for a second course in linear algebra is aimed at undergraduate 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.
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 then introduced, leading to the finite-dimensional spectral theorem and its consequences such as the singular value decomposition. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
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 force in the service of simplicity and clarity; these are also well served by the general precision of Axler's prose... The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library.
The determinant-free proofs are elegant and intuitive.
American Mathematical Monthly
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.
If you liked the previous editions, you will like this new edition even better!
Monatshefte für Mathematik
The print and Kindle versions of this book are available at amazon.com, usually for about $45. Linear Algebra Done Right usually has the best Amazon sales rank of any linear algebra book at this level. Linear Algebra Done Right is usually more than $100 cheaper at Amazon than the book by Friedberg/Insel/Spence, which usually has the second-best Amazon sales rank among linear algebra books at this level.
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ISBN for print version: 978-3-319-11079-0
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