Linear Algebra Done Right - Sheldon Axler

Linear Algebra Done Right

(Autor)

Buch | Hardcover
XVII, 390 Seiten
2023 | 4th ed. 2024
Springer International Publishing (Verlag)
978-3-031-41025-3 (ISBN)
53,49 inkl. MwSt

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



lt;b>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 CalculusAlgebra & 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.

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.

Erscheinungsdatum
Reihe/Serie Undergraduate Texts in Mathematics
Zusatzinfo XVII, 390 p. 33 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Schlagworte adopted textbook • Axler linear algebra • dual spaces • finite-dimensional spectral theorem • linear algebra • open access • Product Spaces • quotient spaces • vector spaces
ISBN-10 3-031-41025-4 / 3031410254
ISBN-13 978-3-031-41025-3 / 9783031410253
Zustand Neuware
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