线性代数(第2版)(英文影印版)

线性代数(第2版)(英文影印版)
分享
扫描下方二维码分享到微信
打开微信,点击右上角”+“,
使用”扫一扫“即可将网页分享到朋友圈。
作者: [美] (Axler,S.)
2008-05
版次: 1
ISBN: 9787506292191
定价: 49.00
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 251页
正文语种: 英语
分类: 自然科学
125人买过
  •   Theaudacioustitleofthisbookdeservesanexplanation.Almostalllinearalgebrabooksusedeterminantstoprovethateverylinearoperatoronafinite-dimensionalcomplexvectorspacehasaneigenvalue.Determinantsaredifficult,nonintuitive,andoftendefinedwithoutmotivation.Toprovethetheoremaboutexistenceofeigenvaluesoncomplexvectorspaces,mostbooksmust.definedeterminants,provethatalinearmapisnotinvertibleffandonlyifitsdeterminantequalsO,andthendefinethecharacteristicpolynomial.Thistortuous(torturous?)pathgivesstudentslittlefeelingforwhyeigenvaluesmustexist.Incontrast,thesimpledeterminant-freeproofspresentedhereoffermoreinsight.Oncedeterminantshavebeenbanishedtotheendofthebook,anewrouteopenstothemaingoaloflinearalgebra--understandingthestructureoflinearoperators. PrefacetotheInstructor
    PrefacetotheStudent
    Acknowledgments
    CHAPTER1
    VectorSpaces
    ComplexNumbers
    DefinitionofVectorSpace
    PropertiesofVectorSpaces
    Subspaces
    SumsandDirectSums
    Exercises

    CHAPTER2
    Finite-DimenslonalVectorSpaces
    SpanandLinearIndependence
    Bases
    Dimension
    Exercises

    CHAPTER3
    LinearMaps
    DefinitionsandExamples
    NullSpacesandRanges
    TheMatrixofaLinearMap
    Invertibility
    Exercises

    CHAPTER4
    Potynomiags
    Degree
    ComplexCoefficients
    RealCoefflcients
    Exercises

    CHAPTER5
    EigenvaluesandEigenvectors
    lnvariantSubspaces
    PolynomialsAppliedtoOperators
    Upper-TriangularMatrices
    DiagonalMatrices
    InvariantSubspacesonRealVectorSpaces
    Exercises

    CHAPTER6
    Inner-Productspaces
    InnerProducts
    Norms
    OrthonormalBases
    OrthogonalProjectionsandMinimizationProblems
    LinearFunctionalsandAdjoints
    Exercises

    CHAPTER7
    OperatorsonInner-ProductSpaces
    Self-AdjointandNormalOperators
    TheSpectralTheorem

    NormalOperatorsonRealInner-ProductSpaces
    PositiveOperators
    Isometries
    PolarandSingular-ValueDecompositions
    Exercises

    CHAPTER8
    OperatorsonComplexVectorSpaces
    GeneralizedEigenvectors
    TheCharacteristicPolynomial
    DecompositionofanOperator
    SquareRoots
    TheMinimalPolynomial
    JordanForm
    Exercises

    CHAPTER9
    OperatorsonRealVectorSpaces
    EigenvaluesofSquareMatrices
    BlockUpper-TriangularMatrices
    TheCharacteristicPolynomial
    Exercises

    CHAPTER10
    TraceandDeterminant
    ChangeofBasis
    Trace
    DeterminantofanOperator
    DeterminantofaMatrix
    Volume
    Exercises
    SymbolIndex
    Index
  • 内容简介:
      Theaudacioustitleofthisbookdeservesanexplanation.Almostalllinearalgebrabooksusedeterminantstoprovethateverylinearoperatoronafinite-dimensionalcomplexvectorspacehasaneigenvalue.Determinantsaredifficult,nonintuitive,andoftendefinedwithoutmotivation.Toprovethetheoremaboutexistenceofeigenvaluesoncomplexvectorspaces,mostbooksmust.definedeterminants,provethatalinearmapisnotinvertibleffandonlyifitsdeterminantequalsO,andthendefinethecharacteristicpolynomial.Thistortuous(torturous?)pathgivesstudentslittlefeelingforwhyeigenvaluesmustexist.Incontrast,thesimpledeterminant-freeproofspresentedhereoffermoreinsight.Oncedeterminantshavebeenbanishedtotheendofthebook,anewrouteopenstothemaingoaloflinearalgebra--understandingthestructureoflinearoperators.
  • 目录:
    PrefacetotheInstructor
    PrefacetotheStudent
    Acknowledgments
    CHAPTER1
    VectorSpaces
    ComplexNumbers
    DefinitionofVectorSpace
    PropertiesofVectorSpaces
    Subspaces
    SumsandDirectSums
    Exercises

    CHAPTER2
    Finite-DimenslonalVectorSpaces
    SpanandLinearIndependence
    Bases
    Dimension
    Exercises

    CHAPTER3
    LinearMaps
    DefinitionsandExamples
    NullSpacesandRanges
    TheMatrixofaLinearMap
    Invertibility
    Exercises

    CHAPTER4
    Potynomiags
    Degree
    ComplexCoefficients
    RealCoefflcients
    Exercises

    CHAPTER5
    EigenvaluesandEigenvectors
    lnvariantSubspaces
    PolynomialsAppliedtoOperators
    Upper-TriangularMatrices
    DiagonalMatrices
    InvariantSubspacesonRealVectorSpaces
    Exercises

    CHAPTER6
    Inner-Productspaces
    InnerProducts
    Norms
    OrthonormalBases
    OrthogonalProjectionsandMinimizationProblems
    LinearFunctionalsandAdjoints
    Exercises

    CHAPTER7
    OperatorsonInner-ProductSpaces
    Self-AdjointandNormalOperators
    TheSpectralTheorem

    NormalOperatorsonRealInner-ProductSpaces
    PositiveOperators
    Isometries
    PolarandSingular-ValueDecompositions
    Exercises

    CHAPTER8
    OperatorsonComplexVectorSpaces
    GeneralizedEigenvectors
    TheCharacteristicPolynomial
    DecompositionofanOperator
    SquareRoots
    TheMinimalPolynomial
    JordanForm
    Exercises

    CHAPTER9
    OperatorsonRealVectorSpaces
    EigenvaluesofSquareMatrices
    BlockUpper-TriangularMatrices
    TheCharacteristicPolynomial
    Exercises

    CHAPTER10
    TraceandDeterminant
    ChangeofBasis
    Trace
    DeterminantofanOperator
    DeterminantofaMatrix
    Volume
    Exercises
    SymbolIndex
    Index
查看详情
相关图书 / 更多
线性代数(第2版)(英文影印版)
线性控制系统的能控性和能观测性(《现代控制系统理论》小丛书)
陈翰馥 执笔;中国科学院数学研究所控制理论研究室编关肇直
线性代数(第2版)(英文影印版)
线性电路及其变换
[苏]H.I.马克西莫维奇著林海明 译
线性代数(第2版)(英文影印版)
线性电路(上册<时域分析>)
[美]R.E.斯科特著郑翔 译
线性代数(第2版)(英文影印版)
线性网络综合理论基础
张有正 编著;陈尚勤
线性代数(第2版)(英文影印版)
线性自动调节系统的过渡过程
會向秋 译;[苏]З.Ш.布洛赫著孙季宽
线性代数(第2版)(英文影印版)
线性系统分析
[美]郑钧著毛培法 译
线性代数(第2版)(英文影印版)
线性代数(计算数学講义 数学基础之 一)
南京大学数学系计算数学专业 编
线性代数(第2版)(英文影印版)
线性规划初步(自然科学知识丛书)
王安琛 著
线性代数(第2版)(英文影印版)
线性不等式与线性规划
A.W.塔凯尔着桂湘云 译;[美]H.W.寇恩
线性代数(第2版)(英文影印版)
线性代数( 高等学校试用教材)
谢邦杰 编
线性代数(第2版)(英文影印版)
线性自动控制系统统计动力学
索洛多夫尼科夫著张东韩 译;[苏]B.B
线性代数(第2版)(英文影印版)
线性代教(高等学校试用教材)
武汉大学数学系数学专业 编