矩阵论引论(introduction to matrix theory)（英文版） / 南京航空航天大学研究生系列精品教材
￥42.00定价
作者： 王正盛
出版社：科学出版社
- 科学出版社
- 9787030453945
- 31
- 158093
- 0045179272-5
- 平装
目录
Contents
Chapter1ReviewandMiscellanea:BasicConceptsinLinearAlgebra1
11MatrixConceptandSpecialMatrices1
12MatrixAlgebra3
13EigenvalueandEigenvector7
14Reading:CayleyandSylvester10
15SelfAssessmentExercises11
Chapter2LinearSpaceandInner-productSpace13
21LinearSpace(VectorSpace)13
22BasisandDimensionofVectorSpace17
23Subspaces20
24InnerProductSpace21
25Reading:GramandSchmidt24
26SelfAssessmentExercises25
Chapter3LinearTransformation27
31Introduction27
32LinearTransformationwithProperties27
33TheRangeandKernel30
34MatrixRepresentationofLinearTransformation32
35Similarity36
36Reading:CramerandGershgorin38
37SelfAssessmentExercises39
Chapter4JordanCanonicalForm41
41Diagonalizability41
42JordanBlockMatrixandJordanFormMatrix44
43-matrixandSmithStandardForm45
44JordanCanonicalForm49
45Cayley-HamiltonTheoremandMinimalPolynomial53
46MATLABCommandsforJordanCanonicalForm55
47Reading:CamilleJordan57
48SelfAssessmentExercises58
Chapter5MatrixFactorization60
51Introduction60
52FullRankDecomposition60
53LUFactorization63
54QRFactorization67
55SchurDecomposition69
56SingularValueDecomposition(SVD)71
57AnExampleofApplication:ImageCompression74
58MATLABCommandsforMatrixFactorization76
59Reading:HouseholderandHouseholderAward78
510SelfAssessmentExercises80
Chapter6HermitianMatrixandPositiveDeˉniteMatrix81
61HermitianMatrix81
62PositiveDeˉniteMatrix84
63Reading:CharlesHermite87
64SelfAssessmentExercises88
Chapter7MatrixNormandMatrixAnalysis89
71Introduction89
72VectorNorm89
73MatrixNorm91
74MatrixSequence，SeriesandFunction94
75MATLABCommandsforNorms98
76Reading:Frobenius99
77SelfAssessmentExercises100
Chapter8TheMoore-PenroseGeneralizedInverse102
81Introduction102
82TheMoore-PenroseGeneralizedInverse102
83TheSolvabilityofLinearSystems105
84MATLABCommandsfortheMoore-PenroseGeneralizedInverseMatrix107
85Reading:MooreandPenrose108
86SelfAssessmentExercises109
Chapter9AnIntroductiontoMATLAB110
91AGlanceofMATLAB110
92StartingUp111
93MATLABasACalculator112
94Plotting119
95Programming122
96CommonlyUsedCommandsSummary127
97Reading:GolubandMoler130
AnswerstoSelectedExercises132
Bibliography149
Chapter1ReviewandMiscellanea:BasicConceptsinLinearAlgebra1
11MatrixConceptandSpecialMatrices1
12MatrixAlgebra3
13EigenvalueandEigenvector7
14Reading:CayleyandSylvester10
15SelfAssessmentExercises11
Chapter2LinearSpaceandInner-productSpace13
21LinearSpace(VectorSpace)13
22BasisandDimensionofVectorSpace17
23Subspaces20
24InnerProductSpace21
25Reading:GramandSchmidt24
26SelfAssessmentExercises25
Chapter3LinearTransformation27
31Introduction27
32LinearTransformationwithProperties27
33TheRangeandKernel30
34MatrixRepresentationofLinearTransformation32
35Similarity36
36Reading:CramerandGershgorin38
37SelfAssessmentExercises39
Chapter4JordanCanonicalForm41
41Diagonalizability41
42JordanBlockMatrixandJordanFormMatrix44
43-matrixandSmithStandardForm45
44JordanCanonicalForm49
45Cayley-HamiltonTheoremandMinimalPolynomial53
46MATLABCommandsforJordanCanonicalForm55
47Reading:CamilleJordan57
48SelfAssessmentExercises58
Chapter5MatrixFactorization60
51Introduction60
52FullRankDecomposition60
53LUFactorization63
54QRFactorization67
55SchurDecomposition69
56SingularValueDecomposition(SVD)71
57AnExampleofApplication:ImageCompression74
58MATLABCommandsforMatrixFactorization76
59Reading:HouseholderandHouseholderAward78
510SelfAssessmentExercises80
Chapter6HermitianMatrixandPositiveDeˉniteMatrix81
61HermitianMatrix81
62PositiveDeˉniteMatrix84
63Reading:CharlesHermite87
64SelfAssessmentExercises88
Chapter7MatrixNormandMatrixAnalysis89
71Introduction89
72VectorNorm89
73MatrixNorm91
74MatrixSequence，SeriesandFunction94
75MATLABCommandsforNorms98
76Reading:Frobenius99
77SelfAssessmentExercises100
Chapter8TheMoore-PenroseGeneralizedInverse102
81Introduction102
82TheMoore-PenroseGeneralizedInverse102
83TheSolvabilityofLinearSystems105
84MATLABCommandsfortheMoore-PenroseGeneralizedInverseMatrix107
85Reading:MooreandPenrose108
86SelfAssessmentExercises109
Chapter9AnIntroductiontoMATLAB110
91AGlanceofMATLAB110
92StartingUp111
93MATLABasACalculator112
94Plotting119
95Programming122
96CommonlyUsedCommandsSummary127
97Reading:GolubandMoler130
AnswerstoSelectedExercises132
Bibliography149
