Authors:
Complete solutions manual available; instructors must contact the author directly by email to obtain the solutions
New edition extensively revised and updated
Covers new topics such as product spaces, quotient spaces, and dual spaces
Features new visually appealing format for both print and electronic versions
Includes almost three times the number of exercises as the previous edition
Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (10 chapters)

Front Matter

Back Matter
About this book
This bestselling textbook for a second course in linear algebra is aimed at undergrad 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 finitedimensional 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.
The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.
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. Innerproduct spaces are introduced, leading to the finitedimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
Keywords
 Axler linear algebra
 adopted textbook
 dual spaces
 finitedimensional spectral theorem
 linear algebra
 product spaces
 quotient spaces
 vector spaces
 matrix theory
Reviews
“This is the third edition of this wellknown introduction to linear algebra. The main changes, apart from the usual improvements during a new edition, are the number of exercises which has more than doubled, new formatting including color printing, new sections on product spaces, quotient spaces, duality, and the chapter on ‘Operators on Real Vector Spaces’ … . if you liked the previous editions, you will like this new edition even better!” (G. Teschl, Monatshefte für Mathematik, 2016)
“This third edition, appearing eighteen years after the second edition, is a further polishing of the existing approach. This book was and still is an interesting and useful text for a second course in linear algebra, concentrating on proofs after the concepts and mechanics have been covered in a first course.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)
AMERICAN MATHEMATICAL MONTHLY
"The determinantfree proofs are elegant and intuitive."
CHOICE
"Every discipline of higher mathematics evinces the profound importance of linear algebra in some way, either for the power derived from its techniques or the inspiration offered by its concepts. 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 forces in the service of simplicity and clarity; these are also well served by the general precision of Axler’s prose. Students with a view towards applied mathematics, analysis, or operator theory will be well served. The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library."
ZENTRALBLATT MATH
"Altogether, the text is a didactic masterpiece."
MATHEMATICAL REVIEWS
"Clarity through examples is emphasized … the text is ideal for class exercises … I congratulate the author and the publisher for a wellproduced textbook on linear algebra."
Authors and Affiliations

Department of Mathematics, San Francisco State University, San Francisco, USA
Sheldon Axler
About the author
Bibliographic Information
Book Title: Linear Algebra Done Right
Authors: Sheldon Axler
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/9783319110806
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2015
Hardcover ISBN: 9783319110790
Softcover ISBN: 9783319307657
eBook ISBN: 9783319110806
Series ISSN: 01726056
Series EISSN: 21975604
Edition Number: 3
Number of Pages: XVII, 340
Number of Illustrations: 26 illustrations in colour
Topics: Linear Algebra