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More About This Textbook
Overview
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents  without having defined determinants  a clean proof that every linear operator on a finitedimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to innerproduct 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. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on selfadjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Editorial Reviews
From the Publisher
FROM THE REVIEWS: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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Meet the Author
Sheldon Axler is Dean of the College of Science & Engineering at San Francisco State University. He has authored many wellreceived books includingPrecalculus: A Prelude to Calculus, Algebra & Trigonometry, College Algebra, A Glimpse at Hilbert Space Operators, Harmonic Function Theory, and Holomorphic Spaces.
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