I am happy to announce that the future fourth edition of Linear Algebra Done Right will be an Open Access book. Thus the electronic version of the book will be legally free to the world. The print version, to be published by Springer, will be reasonably priced.
The electronic and print versions of the fourth edition are currently scheduled to become available in November 2023. Please check this website then.
Chapters 5 and 7 of the future fourth edition of Linear Algebra Done Right are now available below.
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.
Choice
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.
Mathematical Reviews
If you liked the previous editions, you will like this new edition even better!
Monatshefte für Mathematik
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The print and Kindle versions of this book are available at amazon.com. Linear Algebra Done Right usually has the best Amazon sales rank of any linear algebra book at this level. The hardcover version of Linear Algebra Done Right is usually more than $100 cheaper at Amazon than the hardcover version of the book by Friedberg/Insel/Spence, which usually has the second-best Amazon sales rank among linear algebra books at this level.
The print and eBook versions are also available at springer.com.
ISBN for print version: 978-3-319-11079-0
(Linear Algebra Done Right, third edition, in Chinese)linear@axler.net) to request that a review copy be sent from Springer.
Questions or comments about Linear Algebra Done Right can be sent to the author at linear@axler.net.