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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

This best-selling 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 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.

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. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

From reviews of previous editions:

“… a didactic masterpiece”

—Zentralblatt MATH

“… a tour de force in the service of simplicity and clarity … The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library.”

—CHOICE

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

Sheldon Axler is Dean of the College of Science & Engineering at San Francisco State University. He has authored many well-received books including Precalculus: A Prelude to Calculus, Algebra & Trigonometry, College Algebra, A Glimpse at Hilbert Space Operators, Harmonic Function Theory, and Holomorphic Spaces.

Content:
Front Matter....Pages i-xvii
Vector Spaces....Pages 1-26
Finite-Dimensional Vector Spaces....Pages 27-49
Linear Maps....Pages 51-116
Polynomials....Pages 117-130
Eigenvalues, Eigenvectors, and Invariant Subspaces....Pages 131-161
Inner Product Spaces....Pages 163-202
Operators on Inner Product Spaces....Pages 203-240
Operators on Complex Vector Spaces....Pages 241-274
Operators on Real Vector Spaces....Pages 275-294
Trace and Determinant....Pages 295-331
Back Matter....Pages 333-340
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