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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Finkbeiner D.T. — Introduction to Matrices and Linear Transformations |
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| Ïðåäìåòíûé óêàçàòåëü |
 -tuples, ordered 209
-tuples, space of 27 35—36 42
 roots of unity 20 124 140
Abstract systems 1—22 211—212
Abstract systems, homomorphism of 212—213 216—221
Abstract systems, isomorphism of 212—213 217—221
Adjoint 97
Adjoint, determinant of 100
Adjoint, method for  97—99
Alias interpretation 60
Alibi interpretation 60
angle 162 173—181
Annihilator 76
Associativity 7 16—18 49 78
Basis 35—39 58—59
Basis, change of 121
Basis, dual 76
Basis, for idempotent transformations 62
Basis, for nilpotent transformations 148—150
Basis, normal orthogonal 176—180 186 189
Basis, of null space 53
Basis, orthogonal 176
Bessel’s inequality 178
Bilinear form 163—168
Bilinear function 162—168
Bilinear function, conjugate 170
Bilinear function, rank of 164
Bilinearity 49 78 170
Binary operation 14 16 211
Binary relation 209—210
Binomial coefficient 197
Block multiplication 80—83
Boolean algebra 15
Canonical form 107
Canonical form, for congruence 166— 167 187
Canonical form, for equivalence 118 120
Canonical form, for idempotent matrices 125
Canonical form, for nilpotent matrices 152
Canonical form, for row equivalence 115
Canonical form, for similarity 156
Canonical form, for skew-symmetric matrices 166
Canonical form, for symmetric matrices 166—167 187
Canonical form, Jordan 153—158
Cartesian product 8 162 209
Cauchy inequality 172
Cayley — Hamilton theorem see Hamilton — Cayley theorem
Cayley’s Theorem 219
Characteristic, equation 128 131 133 135 206
Characteristic, numbers 127
Characteristic, polynomial 128 133 136 157—159 185
Characteristic, roots 127
Characteristic, values 126— 133 136—141 146 155 185—191 198—202 206-207
Characteristic, vectors 126—133 135—141 185— 186 189 191 201-202
Closed operations 13 17—19 49
Cofactor 95
Column index 64
Column vector 71 77 89 177
Combinatorial equivalence 104 222—228
Commutative group 19
Commutativity 7 16—19 48 68
Complement of a set 6
Complex roots of unity 20 124 140
complex numbers 169—172 189—191
Congruence of integers 219—220
Congruence of matrices 165—168 180 186— 187
Conjugate, -bilinear 170
Conjugate, of a complex matrix 184—185 189
Conjugate, of a complex number 169—172
Conjugate, symmetry 170
Conjunctivity, of matrices 166 190—191
Consistency condition 87
Continuity of a matrix 202
Convergence 193—201
Coordinate system 35—36 (see also Basis)
Coset, of a function 215 220—221
Coset, of a relation 214 220
Cosets, product of 216
Cramer’s Rule 98—99
Cyclic subspace 145
Dantzig, G. B. 222
Derivative of a matrix 202—204
Determinant 88—105 127 204
Determinant, cofactor of a 95
Diagonability of matrices 130—133 136—141 189
Diagonability of quadratic forms 189
Diagonal matrix 69 72 129—132 136—142 166—167 186 189 200
Difference of sets 9
Difference of sets, symmetric 9—10
Difference system 217
Differential equation, infinite 36
Differential equation, matric form of 203 206
Differential equation, of a linear algebra 49
Differential equation, of a vector space 38—40
Differential equation, of subspaces 39—40
Differential equation, solution space of 28 205 207
Dimension, finite 36—37
Direct sum 143—155
Direction numbers 175
Disjoint sets 6
Distance 162 172—173 176—179
Distributivity 7 16
Division algebra 51
Division ring 27
Domain of a function 10 210
Domain of a relation 210
Dot product 165 169 176
Dual, basis 76
Dual, operations 7
Dual, space 75—76 162
Echelon form 111
Echelon form, reduced 112 226
Eigenvalues 127
Eigenvectors 127
Element 4 13
Element, idempotent 16—17
Element, identity 7 16—18 219
Element, inverse 16—18 219
Elementary divisors 157—158
Elementary matrices 108—110 223—228
Elementary operations on matrices 108— 110 117 223—228
Elementary operations on systems of equations 101
Equivalence classes 107 213 215 220 224
Equivalence relations 13 104 106—125 164—168 190—191 213—215 220 222-228
Equivalence relations, combinatorial equivalence 104 222—228
Equivalence relations, congruence 165—168 180
Equivalence relations, conjunctivity 166 190—191
Equivalence relations, equivalence 117—120 122 164—165
Equivalence relations, row equivalence 110—116
Equivalence relations, similarity 120—126 130 136—141 151 156 180 186-187
Equivalent matrices 117—120 122 164
Equivalent systems of equations 101 116 227
Euclidean group 179
Euclidean space 170 173 175—179
Factor system 217
Field 19—22 26
Field, as a vector space 28
Field, finite 20 70 166
Field, of scalar matrices 67 72
Finite field 20 70 166
Finite geometry 3
Finite-dimensional 36—37
Fixed point 127
Form, bilinear 163—168
Form, Hermitian 190— 191
Form, quadratic 182—191
Forsythe, G. E. 100
Frobenius 51
Function 10—13 210—211 220-221
Function, coset of a 215—216 220—221
Function, domain of a 10 210
| Function, of a function 12 45
Function, range of a 10 210
Function, value of a 10
Functions, bilinear 162—168
Functions, hermitian 190
Functions, matrices of 202—204
Functions, of matrices 195—199
Functions, product of 12—13
Functions, quadratic 182—191
Functions, space of continuous 28 170—171
Gram — Schmidt orthogonalization 174—175 178
Group 18—21 26 218—221
Group, commutative 19 26 218
Group, euclidean 179
Group, full linear 57
Group, Lorentz 80
Group, of triangular matrices 72
Hadamard’s inequality 191
Hamilton 51
Hamilton — Cayley theorem 135—136 139 158—161 195
Hermitian, congruence, see Conjunctivity; Hermitian, form 190—191
Hermitian, function 190
Hermitian, matrix 190—191
Hermitian, skew 191
Hermitian, symmetry 170
Homogeneous system 86
Homomorphism, kernel of a 52 221
Homomorphism, of abstract systems 212— 213 217—221
Homomorphism, of vector spaces 41—49
Idempotent element 16—17
Idempotent linear transformation 48 62 75 143—146
Idempotent matrix 70 72 75 125 139
Identity, element 7 16—18 219
Identity, linear transformation 46
Identity, matrix 68
Identity, right 21
Independence, see Linear independence Independent vectors, maximal set of 34
Inequality, Bessel’s 178
Inequality, Cauchy 172
Inequality, Hadamard’s 191
Inequality, Schwarz 171—173
Inequality, triangle 173
Infinite-dimensional 36 171
Inner product 169—182
Inner product, space 170—181
Integral of a matrix 202
Intersection of sets 6 15 17
Intersection of subspaces 30—32
Invariant spaces 54 144—155
Inverse of a matrix, calculation of, by adjoint method 97—99
Inverse of a matrix, calculation of, by approximation 200
Inverse of a matrix, calculation of, by Hamilton — Cayley theorem 159—161
Inverse of a matrix, calculation of, by pivot operations 103—104 227
Inverse of a matrix, calculation of, by row and column operations 118—120
Inverse of a matrix, calculation of, by row operations 113—114
Inverse of a matrix, calculation of, for an orthogonal matrix 180
Inverse, a linear transformation 56
Inverse, element 16—18 219
Inverse, of a mapping 11
Inverse, of a matrix 70 72
Inverse, right 21
Isomorphism, of abstract systems 212—213 217—221
Isomorphism, of matrices and linear transformations 73—76
Isomorphism, of vector spaces 40—43
Jordan canonical form 153—158 196—198 206
Kernel of a homomorphism 52 221
Kronecker delta 68
Latent roots 127
Law of Cosines 177
Left hand notation 45 77 85
Length 162 169 172—179
Linear equations, equivalence of 101 116 227
Linear equations, homogeneous 86
Linear equations, non-homogeneous 86
Linear equations, operations on 100—105
Linear equations, solution by Cramer’s rule 98—99
Linear equations, solution of 84 222
Linear equations, system of 84—89
Linear transformation 44—62
Linear transformation, characteristic values of 126—133 136—141 146 155 185—191 198—202 206-207
Linear transformation, characteristic vectors of 126—133 135—141 185—186 191 201-202
Linear transformation, idempotent 48 62 75 143— 146
Linear transformation, identity 46
Linear transformation, inverse of 56
Linear transformation, Lorentz 79—80
Linear transformation, matric representation of 58—64 73 77 121—124
Linear transformation, negative 46
Linear transformation, nilpotent 48 54 76 133 142—155
Linear transformation, non-singular 55— 57 153
Linear transformation, null space of 52—54 142 153
Linear transformation, nullity of 52—54
Linear transformation, orthogonal 178—182 185—186
Linear transformation, range space of 52—54 114 142 153
Linear transformation, rank of 52—54
Linear transformation, restricted to a subspace 144 149 153
Linear transformation, Segre characteristic of 157—158
Linear transformation, singular 55
Linear transformation, specific form of 57—62
Linear transformation, trace of 160—161
Linear transformation, unitary 179 181
Linear transformation, zero 46
Linear transformations, equality of 45
Linear transformations, product of 45—46
Linear transformations, scalar multiple of 45— 46
Linear transformations, sum of 45—46
Linear, algebra 30 49—51 73—75
Linear, combinations 30
Linear, dependence 32 33
Linear, functional 75—76 162
Linear, group 57
Linear, independence 32— 39 131—132 136 141 146
Linear, programming 101 227
Linear, space; see Vector space Linear equations, consistency condition for 87
Lorentz matrices 79—80
Mac Duffee, C. C. 68
Main diagonal 69
Mapping 10—13 211—221
Mapping, composite 12
Mapping, image under a 10—11 211
Mapping, inverse 11
mapping, many-to-one 11 211
Mapping, of a subspace 48
Mapping, one-to- one 11 211
Mapping, reversible 11
Mapping, zero 13
Mappings, product of 13
Mappings, successive 11 21 215—217
Markov matrix 79 130
Matric polynomial 134
Matrices, block multiplication of 80—83
Matrices, combinatorial equivalence of 104 222—228
Matrices, congruence of 165—168 180 186—187
Matrices, conjunctivity of 166 190—191
Matrices, elementary 108—110 223—228
Matrices, equality of 64
Matrices, equivalence of 117—120 122 164—165
Matrices, functions of 195—199
Matrices, of functions 202— 204
Matrices, product of 66 78
Matrices, row equivalence of 110—116
Matrices, sequences of 193—199
Matrices, similarity of 120—126 130 136—141 151 156 180 186-187
Matrices, sum of 65
Matrix representing a, bilinear function 164
Matrix representing a, linear transformation 58—64 73 77 121—124
Matrix representing a, system of equations 84
Matrix, adjoint of 97
Matrix, augmented 86
Matrix, characteristic equation of 128 131 133 135 206
Matrix, characteristic polynomial of 128 133 136 157—159 185
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