Linear Algebra Done Right (3rd ed)

Linear Algebra Done Right (3rd ed) 下載 mobi epub pdf 電子書 2025

Sheldon Axler
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Springer International Publishing 2014-11-6 Hardcover 9783319110806

具體描述

Sheldon Axler is Dean of the College of Science & Engineering at San Francisco State University. He has authored many well-received books including Precalculus: A Prelude to Calculus, Algebra & Trigonometry, College Algebra, A Glimpse at Hilbert Space Operators, Harmonic Function Theory, and Holomorphic Spaces.

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

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##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。

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##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

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##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

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##第三版加入瞭對偶空間的內容和一些習題,話說另外一本Done wrong也很好~

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##我隻能說這對於中國大部分學生而言不是一本好的教材,對於工科生,很明顯太過於深入,幾乎沒有涉及到應用層麵,比如對角化、SVD分解、QR分解等等的重要應用一概沒有涉及。對於數學係同學,又不夠專業與深入。薄可能隻是第一印象,翻開基本上全是一堆定義、性質、定理、推論的堆...  

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