线性代数（第2版）（英文影印版）

线性代数（第2版）（英文影印版）

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作者: [美] 阿克斯勒（Axler,S.）著

出版社: 世界图书出版公司

出版时间: 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

1 张插图图片

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　　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

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