 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
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 About this Textbook

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.
 About the authors

Sheldon Axler is Dean of the College of Science & Engineering at San Francisco State University. He has authored many wellreceived books including Precalculus: A Prelude to Calculus, Algebra & Trigonometry, College Algebra, A Glimpse at Hilbert Space Operators, Harmonic Function Theory, and Holomorphic Spaces.
 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."
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 Table of contents (10 chapters)


Vector Spaces
Pages 126

FiniteDimensional Vector Spaces
Pages 2749

Linear Maps
Pages 51116

Polynomials
Pages 117130

Eigenvalues, Eigenvectors, and Invariant Subspaces
Pages 131161

Table of contents (10 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Linear Algebra Done Right
 Authors

 Sheldon Axler
 Series Title
 Undergraduate Texts in Mathematics
 Copyright
 2015
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing
 eBook ISBN
 9783319110806
 DOI
 10.1007/9783319110806
 Hardcover ISBN
 9783319110790
 Softcover ISBN
 9783319307657
 Series ISSN
 01726056
 Edition Number
 3
 Number of Pages
 XVII, 340
 Number of Illustrations
 26 illustrations in colour
 Topics