I am happy to announce the publication of the fourth edition of *Linear Algebra Done Right* as an Open Access book. The electronic version of the book is now legally free to the world at the link below.

The print version of the fourth edition of *Linear Algebra Done Right* will be published by Springer in December 2023.

The fourth edition of *Linear Algebra Done Right* contains over 250 new exercises and over 70 new examples, along with several new topics and multiple improvements throughout the book. See page xvi in the file linked above for a list of major improvements and additions in the fourth edition.

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. Determinants are cleanly introduced via alternating multilinear forms.

zbMATH

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

- textbook adoptions: list of 384 universities and colleges that have used Linear Algebra Done Right as a textbook

Follow @AxlerLinear on X (Twitter) for updates on this book.

*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* usually costs considerably less than hardcover versions of competing linear algebra textbooks.

This book is partly based on ideas contained in my paper Down with Determinants!, published in the American Mathematical Monthly. This paper received the Lester R. Ford Award for expository writing from the Mathematical Association of America.

Questions or comments about Linear Algebra Done Right can be sent to the author at `linear@axler.net`

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