线性代数

出版时间：2008-5  出版社：世界图书出版公司  作者：阿克斯勒  页数：251  
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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.

内容概要

　　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.

作者简介

作者：(美国)阿克斯勒(Sheldon Axler)

书籍目录

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

章节摘录

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《线性代数(第2版)(英文影印版)》由世界图书出版公司北京公司出版。

用户评论 (总计12条)

•   印刷 排版 内容 美包包！ 没的说！作者是美国著名数学家用独特的方法教授 线性代数 看完使我们恍然大悟豁然开朗也是美国最受欢迎最好的线性代数教材！
•   各章节条理清晰，概念定义、定理证明严谨，并且阐述动机。课后习题难度适中，主要是加深对本章内容的理解，不是教你怎么计算的。只要仔细读完本章，习题基本都能做。Done Right表明了作者认为线性代数该这么讲，对于想加深理解线性代数的，此书正是你想要的。
•   质量好，印刷也不错，推荐
•   这个话题比较难。这本书很好，但是还需要你自己想好，重视每个页。
•   本书概念清晰透彻，使读者感到抽象的数学有“立体感”。也许线性代数这样来教更好理解。
•   首先，这本书写的是很不错的，但是第三方发货用的全峰快递，收到快递打开看后书已经进水，还有水泡的痕迹，而且我要求开发票的，快递中没有发票，点击补开发票上面说已经开过发票，不知道发票哪里去了。亚马孙直接经营的书是没的说，从发货到送货，我一直都很满意，唯独第三方发货，相当不满意！
•   从独特的（或许是最合适的）角度讲述了向量空间上的线性映射理论，感觉比Lax的书更适合初学者，相对的本作中的内容要少于Lax的书。如果没有在校修过线性代数，可以将本书作为进阶的参考书，但不能代替教材，推荐用Lay的书当做教材。本书能够为学习抽象代数以及泛函分析打下基础，总之极力推荐。PS：中文版的翻译实在不敢恭维 本书对英文的要求也不高 最好还是看这版吧
•   花了一周看完了1～6和9～10章，比较可以！适合回忆！如果我们国内这帮教授能够在书上多花点心思就好了，我上大学那会，线性代数老师用他自己编的教材，结果成了帮忙改错。
•   从线性空间讲起；很清晰；易读；后面算子有点麻烦。
•   在所有的线性代数教材中这本是出类拔萃的。
•   不知道说什么啊.........还比较好吧
•   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... 阅读更多