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
##A self-contained textbook, very constructive.
评分##网络上有很多人把这本书给初学者推荐，我不知道你们究竟读没读过，尤其资质差的初学者，应该连第一章里的很多例子给想不明白。
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##第三版加入了对偶空间的内容和一些习题，话说另外一本Done wrong也很好～
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##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##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##最经典undergraduate advanced linear algebra的教材之一，非常proof-based，不推荐给非数学系的和入门的（calculation-based）
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。
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