線性代數

出版時間:2008-5  出版社:世界圖書出版公司  作者:阿克斯勒  頁數:251  
Tag標簽:無  

前言

You are probably about to teach a course that will give students their second exposure to linear algebra. During their first brush with the subject, your students probably worked with Euclidean spaces and matrices. In contrast, this course will emphasize abstract vector spaces and linear maps.The audacious title of this book deserves an explanation. Almost all linear algebra books use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue.Determinants are difficult, nonintuitive, and often defined without motivation. To prove the theorem about existence of eigenvalues on complex vector spaces, most books must define determinants, prove that a linear map is not invertible if and only ff its determinant equals O, and then define the characteristic polynomial. This tortuous (torturous?) path gives students little feeling for why eigenvalues must exist.In contrast, the simple determinant-free proofs presented here offer more insight. Once determinants have been banished to the end of the book, a new route opens to the main goal of linear algebra-understanding the structure of linear operators.This book starts at the beginning of the subject, with no prerequi-sites other than the usual demand for suitable mathematical maturity.Even if your students have already seen some of the material in the first few chapters, they may be unaccustomed to working exercises of the type presented here, most of which require an understanding of proofs.Vector spaces are defined in Chapter 1, and their basic propertiesare developed.

內容概要

  The audacious title of this book deserves an explanation. Almost all linear algebra books use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue. Determinants are difficult, nonintuitive, and often defined without motivation. To prove the theorem about existence of eigenvalues on complex vector spaces, most books must.define determinants, prove that a linear map is not invertible ff and only if its determinant equals O, and then define the characteristic polynomial. This tortuous (torturous?) path gives students little feeling for why eigenvalues must exist. In contrast, the simple determinant-free proofs presented here offer more insight. Once determinants have been banished to the end of the book, a new route opens to the main goal of linear algebra-- understanding the structure of linear operators.

作者簡介

作者:(美國)阿克斯勒(Sheldon Axler)

書籍目錄

Preface to the InstructorPreface to the StudentAcknowledgmentsCHAPTER 1Vector SpacesComplex NumbersDefinition of Vector SpaceProperties of Vector SpacesSubspacesSums and Direct SumsExercisesCHAPTER 2Finite-Dimenslonal Vector SpacesSpan and Linear IndependenceBasesDimensionExercisesCHAPTER 3Linear MapsDefinitions and ExamplesNull Spaces and RangesThe Matrix of a Linear MapInvertibilityExercisesCHAPTER 4PotynomiagsDegreeComplex CoefficientsReal CoefflcientsExercisesCHAPTER 5Eigenvalues and Eigenvectorslnvariant SubspacesPolynomials Applied to OperatorsUpper-Triangular MatricesDiagonal MatricesInvariant Subspaces on Real Vector SpacesExercisesCHAPTER 6Inner-Product spacesInner ProductsNormsOrthonormal BasesOrthogonal Projections and Minimization Problems Linear Functionals and AdjointsExercisesCHAPTER 7Operators on Inner-Product SpacesSelf-Adjoint and Normal OperatorsThe Spectral TheoremNormal Operators on Real Inner-Product SpacesPositive OperatorsIsometriesPolar and Singular-Value DecompositionsExercisesCHAPTER 8Operators on Complex Vector SpacesGeneralized EigenvectorsThe Characteristic PolynomialDecomposition of an OperatorSquare RootsThe Minimal PolynomialJordan Form  Exercises  CHAPTER 9Operators on Real Vector SpacesEigenvalues of Square MatricesBlock Upper-Triangular MatricesThe Characteristic Polynomial  ExercisesCHAPTER 10Trace and DeterminantChange of BasisTraceDeterminant of an OperatorDeterminant of a MatrixVolumeExercisesSymbol IndexIndex

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《線性代數(第2版)(英文影印版)》由世界圖書出版公司北京公司出版。

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用戶評論 (總計12條)

 
 

  •     印刷 排版 內容 美包包! 沒的說!作者是美國著名數學家用獨特的方法教授 線性代數 看完使我們恍然大悟豁然開朗也是美國最受歡迎最好的線性代數教材!
  •     各章節條理清晰,概念定義、定理證明嚴謹,并且闡述動機。課后習題難度適中,主要是加深對本章內容的理解,不是教你怎么計算的。只要仔細讀完本章,習題基本都能做。Done Right表明了作者認為線性代數該這么講,對于想加深理解線性代數的,此書正是你想要的。
  •     質量好,印刷也不錯,推薦
  •     這個話題比較難。這本書很好,但是還需要你自己想好,重視每個頁。
  •     本書概念清晰透徹,使讀者感到抽象的數學有“立體感”。也許線性代數這樣來教更好理解。
  •     首先,這本書寫的是很不錯的,但是第三方發貨用的全峰快遞,收到快遞打開看后書已經進水,還有水泡的痕跡,而且我要求開發票的,快遞中沒有發票,點擊補開發票上面說已經開過發票,不知道發票哪里去了。亞馬孫直接經營的書是沒的說,從發貨到送貨,我一直都很滿意,唯獨第三方發貨,相當不滿意!
  •     從獨特的(或許是最合適的)角度講述了向量空間上的線性映射理論,感覺比Lax的書更適合初學者,相對的本作中的內容要少于Lax的書。如果沒有在校修過線性代數,可以將本書作為進階的參考書,但不能代替教材,推薦用Lay的書當做教材。本書能夠為學習抽象代數以及泛函分析打下基礎,總之極力推薦。PS:中文版的翻譯實在不敢恭維 本書對英文的要求也不高 最好還是看這版吧
  •     花了一周看完了1~6和9~10章,比較可以!適合回憶!如果我們國內這幫教授能夠在書上多花點心思就好了,我上大學那會,線性代數老師用他自己編的教材,結果成了幫忙改錯。
  •     從線性空間講起;很清晰;易讀;后面算子有點麻煩。
  •     在所有的線性代數教材中這本是出類拔萃的。
  •     不知道說什么啊.........還比較好吧
  •     true mathematical approach and smooth move with induction on propositions and prooves, in the very 1st beginning place this book taught us what is linear, and what is linear... 閱讀更多
 

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