|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Lutkepohl H. — Handbook of Matrices |
|
|
|
| Предметный указатель |
 -norm, properties of 109
 -norm 103
 -norm 103
Absolute norm 102
Absolute value of a matrix 5 39 225
Addition of matrices 3 225
Adjoint of a matrix 6 27 225
Adjugate of a matrix 226
Aitken's integral 152
Annihilating polynomial of a matrix 214 226
Antimetric matrix 226
Arithmetic matrix 226
Asymptotically stable polynomial 212
Band matrix 227
Band matrix, block 227
Banded matrix 227
Bidiagonal matrix 227
Binary matrix 227
Binet — Cauchy formula 49
Binomial formula 37 38
Block matrix 2 229
Block matrix, band 227
Block matrix, circulant 228
Block matrix, companion 220 228
Block matrix, diagonal 229
Block matrix, Hankel 229
Block matrix, properties of 144
Block matrix, Toeplitz 229
Block matrix, triangular 230
Block matrix, tridiagonal 230
Bordered Gramian matrix 230
Bordered matrix 230
Brownian matrix 230
Canonical forms, Choleski decomposition 86
Canonical forms, congruent 85
Canonical forms, diagonal reduction 85
Canonical forms, echelon 88
Canonical forms, Gram — Schmidt triangular reduction 87 92
Canonical forms, Hermite 88 249
Canonical forms, Jordan 83 84 254
Canonical forms, polar decomposition 88
Canonical forms, rank factorization 88
Canonical forms, real Choleski decomposition 92
Canonical forms, real Jordan 89
Canonical forms, real Schur decomposition 92
Canonical forms, Schur decomposition 86
Canonical forms, singular value decomposition 85 91
Canonical forms, Smith 222
Canonical forms, spectral decomposition 85 90
Canonical forms, triangular factorization 87
Cauchy — Schwarz inequality 43 54 104 111
Cayley — Hamilton theorem 67 216
Centro-Hermitian matrix 231
Centro-symmetric matrix 231
Chain rule for derivatives 174 176 202 206
Characteristic determinant of a matrix 12 231
Characteristic equation of a matrix 12 231
Characteristic matrix 220 231
Characteristic polynomial of a matrix 12 63 214 231
Characteristic root 12 63 231
Characteristic root, generalized 245
Characteristic root, in the metric of another matrix 231
Characteristic value 12 63 231
Characteristic value, generalized 245
Characteristic value, in the metric of another matrix 64
Characteristic vector 13 64 232 271
Characteristic vector, in the metric of another matrix 64 232
Check matrix 232 265
Choleski decomposition 86 154
Choleski decomposition of a real matrix 92 155
Circulant matrix 113 232
Circulant matrix, block 228
Circulant matrix, properties of 113
Cofactor matrix 232
Cofactor of an element of a matrix 6 232
Cogredietit matrices 233
Column dimension of a matrix 1 233
Column rank of a matrix 12 233
Column regular matrix 233
Column stochastic matrix 233
Column vector 2 233
Column vectorization of a matrix 233
Column vectorization operator 95
Column-sum norm 103
Column-sum norm, properties of 110
Common divisor of polynomials 212
Common factor of polynomials 212
Common left divisor of polynomial matrices 219 234
Common left divisor of polynomial matrices, greatest 247
Common right divisor of polynomial matrices 219 234
Common right divisor of polynomial matrices, greatest 247
Commutation matrix 9 31 97 115 123 127 234
Commutation matrix, properties of 115
Commuting matrices 234
Companion matrix 213 234
Companion matrix, block 228
Compatible norms 101 235
Complex conjugate matrix 235
Complex matrix 1 235
Compound matrix 235
Condition number of a matrix 236
Conditional inverse matrix 236
Conformable matrices 236
Congruent canonical form of a matrix 85 137
Congruent matrices 236
Conjugate of a matrix 5 24 236
Conjugate transpose of a matrix 5 25 236
Conjunctive matrices 236
Controllability matrix 236
Convergent matrix 119 236 277
Convergent matrix, properties of 119
Convergent polynomial 211
Coprime polynomials 212
Cosine of a matrix 215 236
Courant — Fischer theorem 67 68 133 159
D-inverse 236
Decomposable matrix 237 270
Decomposition of orthogonal matrix 144
Defective matrix 237
Deficient matrix 237
Definite matrix 237
Degree of a polynomial 211
Degree of a polynomial matrix 217 237
Dependent vectors 237
Derivative matrix 237
Derivatives of Hadamard products 184 192 199
Derivatives of inverse matrix 198
Derivatives of Kronecker products 184 192 199
Derivatives of the determinant 181
Derivatives of the trace 177
Derived norm 237
Derogatory matrix 214 237
Determinant 6 47 238
Determinant, Binet — Cauchy formula for 49
Determinant, derivatives of 181
Determinant, inequalities 54
Determinant, Jacobian 173 204
Determinant, of duplication matrix terms 51 53
Determinant, of elimination matrix terms 52 53
Determinant, of partitioned matrix 49
Determinant, optimization of 56
Determinant, Vandermonde 49 283
Diagonal dominant matrix 238
Diagonal matrix 5 9 120 238
Diagonal matrix, block 229
Diagonal matrix, properties of 120
Diagonal of a matrix 238 259
Diagonal reduction of a matrix 60 85
Diagonal similar matrix 238
Diagonalizable matrix 216 238
| Difference of matrices 3 15
Dimension of a matrix 1 239 264
Dimension of a matrix column 233
Dimension of a matrix row 272
Direct product 3 239 279
Direct sum 4 22 239
Divergent polynomial 211
Dividing polynomial 212
Divisibility of a polynomial matrix, left 256
Divisibility of a polynomial matrix, right 271
Divisor, greatest common left 247
Divisor, greatest common right 247
Divisor, of a polynomial 212
Divisor, of a polynomial matrix, left 256
Divisor, of a polynomial matrix, right 271
Dominating 239
Dominating nonnegative matrix 239
Dominating principal diagonal 239
Dominating, principal 2
Dominating, secondary 273
Doubly centered matrix 239
Doubly quasi-stochastic matrix 240
Doubly stochastic matrix 139 240
Drazin inverse 240
Duplication matrix 9 31 51 53 97 118 122 127 130 157 165 240
Duplication matrix, properties of 122 149
Dyadic product 241
Echelon form 88 241
Effective inverse matrix 241
Eigenvalue 12 63 64
Eigenvalue, algebraic multiplicity 226
Eigenvalue, generalized 245
Eigenvalue, geometric multiplicity 246
Eigenvalue, Hopf's theorem for 142
Eigenvalue, in the metric of another matrix 64 241
Eigenvalue, inclusion principle 73 135 160
Eigenvalue, inequalities 72 134 159
Eigenvalue, multiplicity of 262
Eigenvalue, of a Hermitian matrix 133
Eigenvalue, of a matrix 241
Eigenvalue, of a polynomial matrix 218 241
Eigenvalue, of a positive definite matrix 153
Eigenvalue, of a symmetric matrix 158
Eigenvalue, Poincare's separation theorem 74 136 161
Eigenvalue, simple 63 275
Eigenvalue, Weyl's theorem 75 136 162
Eigenvector 13 64 242 271
Eigenvector matrix 241 261
Eigenvector, generalized 245
Eigenvector, in the metric of another matrix 64 242
Eigenvector, left 256
Eigenvector, right 271
Elementary divisors of a polynomial matrix 220 242
Elementary matrix 242
Elementary operations 12
Elementary operations, for a matrix 242
Elementary operations, for a polynomial matrix 219 242
Elementary polynomial matrix 219 242
Elements of a matrix 1
Elementwise product 3 243
Elimination matrix 9 31 52 53 97 118 123 126 127 165 243
Elimination matrix, properties of 127
Entries of a matrix 1
EP-matrix 243
Equality of matrices 243
Equivalent matrices 243
Equivalent polynomial matrices 220 243
Ergodic matrix 243
Euclidean norm 103
Euclidean norm, properties of 109
Exchange matrix 243 270
Exponential function of a matrix 215 244
Exponential matrix 244
Factor of a polynomial 212
Fischer's inequality for determinants 54 147 152
Flip matrix 244 270
Fourier matrix 114 244
Frobenius inequality 61
Frobenius matrix 244
Frobenius norm 103
Function of a matrix 259
g-circulant matrix 245
G-inverse matrix 245
Generalized characteristic root 245
Generalized characteristic value 245
Generalized eigenvalue 245
Generalized eigenvector of a matrix 245
Generalized inverse of a matrix 7 32 245 269
Generalized inverse rule for derivatives 209
Generalized permutation matrix 140 245
Geometric matrix 246
Geometric multiplicity of an eigenvalue 246
Givens matrix 246
Gradient matrix 246
Gradient vector 171 174 247
Gram matrix 247
Gram — Schmidt triangular reduction of a matrix 87
Gram — Schmidt triangular reduction of a nortsirtgular matrix 87
Gram — Schmidt triangular reduction of a real matrix 92
Gram — Schmidt triangular reduction of a real nonsingular matrix 92
Gram — Schmidt triangular reduction of a real square matrix 92
Gram — Schmidt triangular reduction of a square matrix 87
Gramian matrix 247
Gramian matrix, bordered 230
Greatest common divisor of polynomials 212
Greatest common factor of polynomials 212
Greatest common left divisor of polynomial matrices 219 247
Greatest common right divisor of polynomial matrices 219 247
Group inverse of a matrix 247
Hadamard matrix 247
Hadamard product 3 20 248
Hadamard product, derivatives of 184 192 199
Hadamard's inequality 54
Half-vectorization of a matrix 8 96 248
Half-vectorization operator 96 248
Hamiltonian matrix 248
Hankel matrix 249 265
Hankel matrix, block 229
Harmonic matrix 249
Helmert matrix 249
Hermite canonical form 88 249
Hermitian adjoint of a matrix 5 250
Hermitian form 12 250
Hermitian form, negative definite 262
Hermitian form, negative semidefinite 262
Hermitian form, positive definite 267
Hermitian form, positive semidefinite 267
Hermitian matrix 10 131 250
Hermitian matrix, decomposition of 137
Hermitian matrix, eigenvalues of 133
Hermitian matrix, properties of 131
Hessenberg matrix 250 283
Hessenberg matrix, lower 258
Hessian matrix 172 175 250
Hessian matrix, of the log determinant 182
Hessian matrix, of the trace 179
Hilbert matrix 251
Hilbert — Schmidt norm 103
Hoelder's inequality 44 111
Hopf's theorem for eigenvalues 78 142
Householder transformation 132 168 251
Hurwitz matrix 214 251
Hurwitz theorem 217
Idempotent matrix 10 138 251
Idempotent matrix, properties of 138
Identity matrix 2 10 252
Imaginary matrix 252
Imprimitive matrix 252
Inclusion principle for eigenvalues 73 135 160
Indefinite matrix 252
|
|
|
| Реклама |
|
|
|
|
|
О проекте