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
这是一本我愿意用“优美”去形容的数学书，纯粹的数学思维，完全不考虑应用。作者好心地公布了习题答案，http://linearalgebras.com/
评分##Mediocre textbook.
评分##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##好多人打三星的理由都是这本书不适合初学者学...但是这个不是从目录就看得出来吗 跳过传统教材中的矩阵/行列式直接从线性空间/映射的角度入手我觉得对于后面进阶内容的学习很有帮助啊 况且大部分的线代教材不太会讲quotient space, duality, spectral theorem之类的吧 正如某位网友评论所道 “用泛函分析降维攻击线性代数” 这本书如果拿来第二遍复习巩固的话会发现整个体系非常漂亮
评分##对比了第三版和第二版的第五章，第三版易读多了 didn't enjoy it as much as I expected. found<linear algebra with geometric applications by larry mansfield> in library instead. the latter structures in a way more comprehensive and straightforward, at least for me.
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##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##思路可取，但是公式推导太多了，不易于构建直观印象，线性代数本身和几何联系很多，公式定理和几何意义一块走才是好的。
评分##用泛函分析降维攻击线性代数
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