高等线性代数(第3版)
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23
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69
八五品
库存2件
作者[美]罗曼 著
出版社世界图书出版公司
出版时间2008-08
版次1
装帧平装
上书时间2024-07-19
商品详情
- 品相描述:八五品
图书标准信息
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作者
[美]罗曼 著
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出版社
世界图书出版公司
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出版时间
2008-08
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版次
1
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ISBN
9787506292528
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定价
69.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
522页
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正文语种
英语
- 【内容简介】
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isathoroughintroductiontolinearalgebra,forthegraduateoradvancedundergraduatestudent。Prerequisitesarelimitedtoaknowledgeofthebasicpropertiesofmatricesanddeterminants。However,sincewecoverthebasicsofvectorspacesandlineartransformationsratherrapidly,apriorcourseinlinearalgebra(evenatthesophomorelevel),alongwithacertainmeasureof"mathematicalmaturity,"ishighlydesirable。
- 【作者简介】
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暂无......
- 【目录】
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PrefacetotheThirdEdition,vii
PrefacetotheSecondEdition,ix
PrefacetotheFirstEdition,xi
Preliminaries
Part1:Preliminaries
Part2:AlgebraicStructures
PartI-BasicLinearAlgebra
1VectorSpaces
VectorSpaces
Subspaces
DirectSums
SpanningSetsandLinearIndependence
TheDimensionofaVectorSpace
OrderedBasesandCoordinateMatrices
TheRowandColumnSpacesofaMatrix
TheC0mplexificationofaRealVectorSpace
Exercises
2LinearTransformations
LinearTransformations
TheKernelandImageofaLinearTransformation
Isomorphisms
TheRankPlusNullityTheorem
LinearTransformationsfromFntoFm
ChangeofBasisMatrices
TheMatrixofaLinearTransformation
ChangeofBasesforLinearTransformations
EquivalenceofMatrices
SimilarityofMatrices
SimilarityofOperators
InvariantSubspacesandReducingPairs
ProjectionOperators
TopologicalVectorSpaces
LinearOperatorsonVc
Exercises
3TheIsomorphismTheorems
QuotientSpaces
TheUniversalPropertyofQuotientsandtheFirstIsomorphismTheorem
QuotientSpaces,ComplementsandCodimension
AdditionalIsomorphismTheorems
LinearFunctionals
DualBases
Reflexivity
Annihilators
OperatorAdjoints
Exercises
4ModulesI:BasicProperties
Motivation
Modules
Submodules
SpanningSets
LinearIndependence
TorsionElements
Annihilators
FreeModules
Homomorphisms
QuotientModules
TheCorrespondenceandIsomorphismTheorems
DirectSumsandDirectSummands
ModulesAreNotasNiceasVectorSpaces
Exercises
5ModulesII:FreeandNoetherianModules
TheRankofaFreeModule
FreeModulesandEpimorphisms
NoetherianModules
TheHilbertBasisTheorem
Exercises
6ModulesoveraPrincipalIdealDomain
AnnihilatorsandOrders
CyclicModules
FreeModulesoveraPrincipalIdealDomain
Torsion-FreeandFreeModules
ThePrimaryCyclicDecompositionTheorem
TheInvariantFactorDecomposition
CharacterizingCyclicModules
lndecomposableModules
Exercises
IndecomposableModules
Exercises159
7TheStructureofaLinearOperator
TheModuleAssociatedwithaLinearOperator
ThePrimaryCyclicDecompositionofVT
TheCharacteristicPolynomial
CyclicandIndecomposableModules
TheBigPicture
TheRationalCanonicalForm
Exercises
8EigenvaluesandEigenvectors
EigenvaluesandEigenvectors
GeometricandAlgebraicMultiplicities
TheJordanCanonicalForm
TriangularizabilityandSchursTheorem
DiagonalizableOperators
Exercises
9RealandComplexInnerProductSpaces
NormandDistance
Isometrics
Orthogonality
OrthogonalandOrthonormalSets
TheProjectionTheoremandBestApproximations
TheRieszRepresentationTheorem
Exercises
10StructureTheoryforNormalOperators
TheAdjointofaLinearOperator
OrthogonalProjections
UnitaryDiagonalizability
NormalOperators
SpecialTypesofNormalOperators
Seif-AdjointOperators
UnitaryOperatorsandIsometries
TheStructureofNormalOperators
FunctionalCalculus
PositiveOperators
ThePolarDecompositionofanOperator
Exercises
PartⅡ-Topics
11MetricVectorSpaces:TheTheoryofBilinearForms
SymmetricSkew-SymmetricandAlternateForms
TheMatrixofaBilinearForm
QuadraticForms
Orthogonality
LinearFunctionals
OrthogonalComplementsandOrthogonalDirectSums
Isometrics
HyperbolicSpaces
NonsingularCompletionsofaSubspace
TheWittTheorems:APreview
TheClassificationProblemforMetricVectorSpaces
SymplecticGeometry
TheStructureofOrthogonalGeometries:OrthogonalBases
TheClassificationofOrthogonalGeometries:CanonicalForms
TheOrthogonalGroup
TheWittTheoremsforOrthogonalGeometries
MaximalHyperbolicSubspacesofanOrthogonalGeometry
Exercises
12MetricSpaces
TheDefinition
OpenandClosedSets
ConvergenceinaMetricSpace
TheClosureofaSet
DenseSubsets
Continuity
Completeness
Isometrics
TheCompletionofaMetricSpace
Exercises
13HilbertSpaces
ABriefReview
HilbertSpaces
InfiniteSeries
AnApproximationProblem
HilbertBases
FourierExpansions
ACharacterizationofHilbertBases
HilbertDimension
ACharacterizationofHilbertSpaces
TheRieszRepresentationTheorem
Exercises
14TensorProducts
Universality
BilinearMaps
TensorProducts
WhenIsaTensorProductZero?
CoordinateMatricesandRank
CharacterizingVectorsinaTensorProduct
DefiningLinearTransformationsonaTensorProduct
TheTensorProductofLinearTransformations
ChangeofBaseField
MultilinearMapsandIteratedTensorProducts
TensorSpaces
SpecialMultilinearMaps
GradedAlgebras
TheSymmetricandAntisymmetricTensorAlgebras
TheDeterminant
Exercises
15PositiveSolutionstoLinearSystems:ConvexityandSeparation
ConvexClosedandCompactSets
ConvexHulls
LinearandAffineHyperplanes
Separation
Exercises
16AffineGeometry
AffineGeometry
AffineCombinations
AffineHulls
TheLatticeofFlats
AffineIndependence
AffineTransformations
ProjectiveGeometry
Exercises
17SingularValuesandtheMoore-PenroseInverse
SingularValues
TheMoore-PenroseGeneralizedInverse
LeastSquaresApproximation
Exercises
18AnIntroductiontoAlgebras
Motivation
AssociativeAlgebras
DivisionAlgebras
Exercises
19TheUmbralCalculus
FormalPowerSeries
TheUmbralAlgebra
FormalPowerSeriesasLinearOperators
ShefferSequences
ExamplesofShefferSequences
UmbralOperatorsandUmbralShifts
ContinuousOperatorsontheUmbralAlgebra
OperatorAdjoints
UmbralOperatorsandAutomorphismsoftheUmbralAlgebra
UmbralShiftsandDerivationsoftheUmbralAlgebra
TheTransferFormulas
AFinalRemark
Exercises
References
IndexofSymbols
Index
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