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 systematic re-learning
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##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##（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##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。
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。
