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
##網上有這書配套視頻。可以認為是第二門綫性代數課程的教材吧。 啥時候網上再搬運個advanced linear algebra的課程，達到peter lax那本書的難度，那豈不是都齊活瞭。 都是一個主題，有工科的、有數學的；有偏理論的，有偏應用和計算的，還有結閤具體學科講的，果然是得多找資源，反復學纔能有所得。
評分##其實綫性代數也不能這樣學……正文全是引理、定理和推論的堆砌，課後習題量較大且比較刁鑽，並不是很利於鞏固所學的內容。學下來的體會就是：雖然刷瞭幾百道習題，但兩個月一過正文的內容就已經忘得差不多瞭。
評分##（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##開始刷習題
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##A self-contained textbook, very constructive.
評分##網絡上有很多人把這本書給初學者推薦，我不知道你們究竟讀沒讀過，尤其資質差的初學者，應該連第一章裏的很多例子給想不明白。
評分##對比瞭第三版和第二版的第五章，第三版易讀多瞭 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.
評分##非常推薦
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