Linear Algebra Done Right

基本信息

Series:Undergraduate Texts in Mathematics

Format:Hardback 390 pages, 33 Illustrations, color; XVII, 390 p. 33 illus. in color.

Publisher:Springer International Publishing AG

Imprint:Springer International Publishing AG

Edition:4th ed. 2024

ISBN:9783031410253

Published:20 Nov 2023

Weight:706g

Dimensions:160 x 243 x 24 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

这本线性代数第二课的畅销教科书面向数学专业的本科生和研究生。第四版对奇异值分解及其后果进行了扩展处理。新版增加了关于多线性代数的一章，涉及双线性方程组、二次方程组、张量积以及通过交替多线性方程组求行列式的方法。

新版还增加了小多项式的使用，为多个结果提供了更简洁的证明。此外，还新增了 250 多道习题。本书采用的新方法将行列式放到了书末。

这本书的重点是线性代数的核心目标：理解有限维向量空间上线性算子的结构。作者特别注意激发概念和简化证明。每章都有各种有趣的练习，帮助学生理解和操作线性代数的对象。

无论是印刷版还是电子版，精美的格式使页面的外观对学生异常友好。除了通常所要求的适当的数学成熟度之外，不假定任何先决条件。课文先讨论了向量空间、线性独立性、跨度、基础和维度。

然后，本书讨论了线性映射、特征值和特征向量。书中介绍了内积空间，并引出了有限维谱定理及其后果。然后使用广义特征向量来深入探讨线性算子的结构。

前版本的评论：“总之，这本书是一部教学杰作。无行列式证明优雅而直观。《美国数学月刊》多年来新颖的线性代数书籍，它肯定属于每一个本科生。”

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 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

作者简介

谢尔顿·埃克斯勒(Sheldon Axler)是旧金山州立大学科学与工程学院院长。他撰写了许多广受欢迎的书籍，包括微积分前期:微积分的序曲，代数与三角，大学代数，希尔伯特空间算子的一瞥，调和函数理论，和全纯空间。

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.