Linear Algebra Done Right

Sheldon Axler

I am happy to announce publication of the fourth edition of Linear Algebra Done Right as an Open Access book. The electronic version of this new fourth edition with a Creative Commons BY-NC license is availble without cost at the link below.

The print version of the new fourth edition of Linear Algebra Done Right is available from Amazon at the link below.

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.

Excerpts from Reviews

Altogether, the text is a didactic masterpiece.

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.
Mathematical Reviews

If you liked the previous editions, you will like this new edition even better!
Monatshefte für Mathematik

user reviews from Amazon

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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

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