Sheldon Axler

Linear Algebra Done Right

• Gebundenes Buch

Produktbeschreibung

Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added.

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 simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions.

No prerequisites are assumed other than the usual demand for suitable mathematical maturity. 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 the reviews of previous editions:

Altogether, the text is a didactic masterpiece. - zbMATH

The determinant-free proofs are elegant and intuitive. - American Mathematical Monthly

The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library - CHOICE

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Produktdetails

• Undergraduate Texts in Mathematics
• Verlag: Sheldon Axler / Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-031-41025-3
• 4. Aufl.
• Seitenzahl: 390
• Erscheinungstermin: 20. November 2023
• Englisch
• Abmessung: 22mm x 217mm x 246mm
• Gewicht: 705g
• ISBN-13: 9783031410253
• Artikelnr.: 68377520

Autorenporträt

Sheldon Axler, Professor Emeritus of the Mathematics Department at San Francisco State University, has authored many well-received books including
Linear Algebra Done Right (in four editions) Measure, Integration & Real Analysis (Open Access) Precalculus: A Prelude to Calculus, Algebra & Trigonometry (in three editions)College Algebra Harmonic Function Theory (in two editions).
Axler has served as Editor-in-Chief of the Mathematical Intelligencer and Associate Editor of the American Mathematical Monthly. He has been a member of the Council of the American Mathematical Society and a member of the Board of Trustees of the Mathematical Sciences Research Institute. He is a Fellow of the American Mathematical Society and has been a recipient of numerous grants from the National Science Foundation.

Inhaltsangabe

Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces.- 2. Finite-Dimensional Vector Spaces.- 3. Linear Maps.- 4. Polynomials.- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces.- 6. Inner Product Spaces.- 7. Operators on Inner Product Spaces.- 8. Operators on Complex Vector Spaces.- 9. Operators on Real Vector Spaces.- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.

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-Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces- 2. Finite-Dimensional Vector Spaces- 3. Linear Maps- 4. Polynomials- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces- 6. Inner Product Spaces- 7. Operators on Inner Product Spaces- 8. Operators on Complex Vector Spaces- 9. Operators on Real Vector Spaces- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.

Rezensionen

"This is the third edition of this well-known 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 determinant-free 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 well-produced textbookon linear algebra."