线性代数（第2版）（英文影印版）

图书标准信息

• 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元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 251页
• 正文语种 英语

【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