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题名/责任者:

Linear algebra done right / Sheldon Axler.

版本说明:

Fourth edition.

出版发行项:

Cham, Switzerland : Springer, [2024]

出版发行项:

?2024

ISBN:

3031410254

ISBN:

9783031410253

载体形态项:

xvii, 390 pages : color illustrations ; 25 cm.

丛编说明:

Undergraduate texts in mathematics, 0172-6056

丛编统一题名:

Undergraduate texts in mathematics.

个人责任者:

Axler, Sheldon Jay, author.

论题主题:

Algebras, Linear-Textbooks.

论题主题:

Algebras, Linear.

中图法分类号:

O151.2

一般附注:

Includes indexes.

内容附注:

1. Vector Spaces -- 2. Finite-Dimensional Vector Spaces -- 3. Linear Maps -- 4. Polynomials -- 5. Eigenvalues and Eigenvectors -- 6. Inner Product Spaces -- 7. Operators on Inner Product Spaces -- 8. Operators on Complex Vector Spaces -- 9. Multilinear Algebra and Determinants.

摘要附注:

"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." --

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