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##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##慕名而來，看瞭後認為這本書不適閤工科生看，而是專門給數學係的學生看得。 書的內容結構是從最基本定義、概念開始，通過一步一步的邏輯推理産生各個定理和綫性代數一係列的性質，有點類似於幾何原本的敘述結構。 對於數學極差的我來說，前7章還算可以勉強看的懂，後麵幾章大量符號、概念、定理都揉雜在一起(這些應該是這本書的高潮)就基本濛瞭，也就導緻自己匆匆略過瞭，也沒有耐心看下去瞭
評分##a systematic re-learning
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##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##（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##a systematic re-learning
相關圖書
本站所有內容均為互聯網搜尋引擎提供的公開搜索信息，本站不存儲任何數據與內容，任何內容與數據均與本站無關，如有需要請聯繫相關搜索引擎包括但不限於百度，google,bing,sogou 等
© 2026 windowsfront.com All Rights Reserved. 靜流書站 版權所有