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)
具體描述
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
用戶評價
##（碩士期間上矩陣分析課時看過一部分）這本書的視角比較偏數學係，完全以最抽象的方式來構建整個綫代知識體係。本書可以改名為《如何重新理解綫性代數》。適閤作為綫代進階。
評分這是一本我願意用“優美”去形容的數學書，純粹的數學思維，完全不考慮應用。作者好心地公布瞭習題答案，http://linearalgebras.com/
評分##Mediocre textbook.
評分##思路可取，但是公式推導太多瞭，不易於構建直觀印象，綫性代數本身和幾何聯係很多，公式定理和幾何意義一塊走纔是好的。
評分##這本書真的不適閤初學者，前兩章隻是讓你看著很美好。
評分##其實19年就買瞭這本書。當時幾乎沒有一頁能吸收。經過兩三年的自學數學，提高瞭數學成熟性，突然發現，能看懂瞭甚至能體會其美妙瞭。不過即使是數學係的，單獨這本書也是太過抽象，還是應該佐一本偏工科的高階綫性代數以獲得一些geometrical intuition.
評分##真的是越學越覺得Axler這本問題大，正文材料太簡單然後練習題的難度又完全不相稱。所謂的一開始就從抽象概念（Linear map)而不是傳統的Matirx講起確實是不錯，不過因為各個材料平均施力完全看不齣重點可以說是最大的敗筆。強烈不建議隻看這本，如果想學好Lin alg應該再加那本fin dim vector spaces， 對dual, spectrum theorem, Jordan form還有matrix的理解會好很多。
評分##好多人打三星的理由都是這本書不適閤初學者學...但是這個不是從目錄就看得齣來嗎 跳過傳統教材中的矩陣/行列式直接從綫性空間/映射的角度入手我覺得對於後麵進階內容的學習很有幫助啊 況且大部分的綫代教材不太會講quotient space, duality, spectral theorem之類的吧 正如某位網友評論所道 “用泛函分析降維攻擊綫性代數” 這本書如果拿來第二遍復習鞏固的話會發現整個體係非常漂亮
評分##A self-contained textbook, very constructive.
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