Front Matter....Pages i-xvii
Vector Spaces....Pages 1-26
Finite-Dimensional Vector Spaces....Pages 27-49
Linear Maps....Pages 51-116
Polynomials....Pages 117-130
Eigenvalues, Eigenvectors, and Invariant Subspaces....Pages 131-161
Inner Product Spaces....Pages 163-202
Operators on Inner Product Spaces....Pages 203-240
Operators on Complex Vector Spaces....Pages 241-274
Operators on Real Vector Spaces....Pages 275-294
Trace and Determinant....Pages 295-331
Back Matter....Pages 333-340
· · · · · · (收起)
具体描述
New edition extensively revised and updated
Covers new topics such as product spaces, quotient spaces, and dual spaces
Features new visually appealing format for both print and electronic versions
Includes almost three times the number of exercises as the previous edition
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. 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 to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.
The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.
No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus 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 reviews of previous editions:
“… a didactic masterpiece”
—Zentralblatt MATH
“… a tour de force in the service of simplicity and clarity … The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library.”
—CHOICE
The determinant-free proofs are elegant and intuitive.
—American Mathematical Monthly
“Clarity through examples is emphasized … the text is ideal for class exercises … I congratulate the author and the publisher for a well-produced textbook on linear algebra.”
—Mathematical Reviews
用户评价
##慕名而来，看了后认为这本书不适合工科生看，而是专门给数学系的学生看得。 书的内容结构是从最基本定义、概念开始，通过一步一步的逻辑推理产生各个定理和线性代数一系列的性质，有点类似于几何原本的叙述结构。 对于数学极差的我来说，前7章还算可以勉强看的懂，后面几章大量符号、概念、定理都揉杂在一起(这些应该是这本书的高潮)就基本蒙了，也就导致自己匆匆略过了，也没有耐心看下去了
评分##这本书真的不适合初学者，前两章只是让你看着很美好。
评分##A self-contained textbook, very constructive.
评分##其实19年就买了这本书。当时几乎没有一页能吸收。经过两三年的自学数学，提高了数学成熟性，突然发现，能看懂了甚至能体会其美妙了。不过即使是数学系的，单独这本书也是太过抽象，还是应该佐一本偏工科的高阶线性代数以获得一些geometrical intuition.
评分##其实19年就买了这本书。当时几乎没有一页能吸收。经过两三年的自学数学，提高了数学成熟性，突然发现，能看懂了甚至能体会其美妙了。不过即使是数学系的，单独这本书也是太过抽象，还是应该佐一本偏工科的高阶线性代数以获得一些geometrical intuition.
评分##其实线性代数也不能这样学……正文全是引理、定理和推论的堆砌，课后习题量较大且比较刁钻，并不是很利于巩固所学的内容。学下来的体会就是：虽然刷了几百道习题，但两个月一过正文的内容就已经忘得差不多了。
评分##Mediocre textbook.
评分##其实线性代数也不能这样学……正文全是引理、定理和推论的堆砌，课后习题量较大且比较刁钻，并不是很利于巩固所学的内容。学下来的体会就是：虽然刷了几百道习题，但两个月一过正文的内容就已经忘得差不多了。
评分##真的是越学越觉得Axler这本问题大，正文材料太简单然后练习题的难度又完全不相称。所谓的一开始就从抽象概念（Linear map)而不是传统的Matirx讲起确实是不错，不过因为各个材料平均施力完全看不出重点可以说是最大的败笔。强烈不建议只看这本，如果想学好Lin alg应该再加那本fin dim vector spaces， 对dual, spectrum theorem, Jordan form还有matrix的理解会好很多。
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