Linear Algebra Done Right

second edition

Sheldon Axler

This text, published by Springer, is intended for a second course in linear algebra. The novel approach used throughout the book takes great care to motivate concepts and simplify proofs. For example, the book presents, without having defined determinants, a clean proof that every linear operator on a finite-dimensional complex vector space (or on an odd-dimensional real vector space) has an eigenvalue.

Although this text is intended for a second course in linear algebra, there are no prerequisites other than appropriate mathematical maturity. Thus the book starts by discussing vector spaces, linear independence, span, basis, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem.

A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.

Excerpts from Reviews

Altogether, the text is a didactic masterpiece.
Zentralblatt für Mathematik

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

Third Edition is Coming

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Softcover: $44.95 (although usually available for less at, ISBN 978-0-387-98258-8.
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Hardcover: $79.95 (although usually available for less at, ISBN 978-0-387-98259-5.
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This book is partly based upon 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.
Faculty who are seriously interested in using this book as a text can contact me ( to request that a review copy be sent from Springer.
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