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
##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##a systematic re-learning
评分这是一本我愿意用“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##开始刷习题
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##（硕士期间上矩阵分析课时看过一部分）这本书的视角比较偏数学系，完全以最抽象的方式来构建整个线代知识体系。本书可以改名为《如何重新理解线性代数》。适合作为线代进阶。
评分这是一本我愿意用“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##网上有这书配套视频。可以认为是第二门线性代数课程的教材吧。 啥时候网上再搬运个advanced linear algebra的课程，达到peter lax那本书的难度，那岂不是都齐活了。 都是一个主题，有工科的、有数学的；有偏理论的，有偏应用和计算的，还有结合具体学科讲的，果然是得多找资源，反复学才能有所得。
评分##Mediocre textbook.
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