Böcker av Sheldon Axler

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. -- zbMATHThe determinant-free proofs are elegant and intuitive. -- American Mathematical MonthlyThe most original linear algebra book to appear in years, it certainly belongs in every undergraduate library -- CHOICE

This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces.

College Algebra, First Edition will appeal to those who want to give important topics more in-depth, higher-level coverage. This text offers streamlined approach accompanied with accessible definitions across all chapters to allow for an easy-to-understand read.

College Algebra and Trigonometry will appeal to those who want to give important topics more in-depth, higher-level coverage. This text offers streamlined approach accompanied with accessible definitions across all chapters to allow for an easy-to-understand read.

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis.