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| Авторизация |
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| Поиск по указателям |
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| Lutkepohl H. — Handbook of Matrices |
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| Предметный указатель |
Independent vectors 252
Index of a square matrix 252
Induced matrix norm 102 252 264
Induced matrix norm, properties of 108
Inequalities, Cauchy — Schwarz 43 54 104 111
Inequalities, Fischer's 54 147 152
Inequalities, for eigenvalues 72 134 159
Inequalities, for norms 111
Inequalities, Frobenius 61
Inequalities, Hadamard's 54
Inequalities, Hoelder's 44 111
Inequalities, Minkowski's 44 55
Inequalities, Oppenheim's 56
Inequalities, Ostrowski — Taussky 56
Inequalities, Schur's 43
Inequalities, singular value 80
Inequalities, Sylvester's 61
Inequalities, triangle 101
Inequality relations for matrices 4
Inertia of a square matrix 252
Inner product 102 252
Inner product over the complex numbers 102
Inner product over the real numbers 102 253
Inner product, special 104
Integer matrix 253
Integer matrix, unimodular 281
Integral matrix 253
Invariant factors of a polynomial matrix 220 253
Invariant polynomials of a polynomial matrix 220 253
Inverse matrix 7 27 253
Inverse matrix, conditional 236
Inverse matrix, derivatives of 198
Inverse matrix, Drazin 240
Inverse matrix, effective 241
Inverse matrix, g- 245
Inverse matrix, generalized 32 245
Inverse matrix, left 257
Inverse matrix, Moore — Penrose 34 262
Inverse matrix, MP- 262
Inverse matrix, partitioned 29
Inverse matrix, pseudo 269
Inverse matrix, reflexive generalized 270
Inverse matrix, right 271
Invertible matrix 10 253 263 270
Invertible polynomial matrix 218 254
Involutory matrix 254
Irreducible matrix 254
Isometry for a norm 101 254
Jacobian determinant 173 204
Jacobian matrix 173 183 254
Jordan canonical form 254
Jordan decomposition 63 70 71 83 89
Jordan decomposition, near diagonal 84
Jordan decomposition, of a real matrix with real eigenvalues 89
Jordan decomposition, real 71 89
Jordan Matrix 255
Jordan normal form 254
Kronecker matrix 255
Kronecker product 3 19 117 124 126 128 130 256
Kronecker product, derivatives of 184 192 199
Kronecker sum 256
Latent root of a matrix 12 63 256
Latent root of a polynomial matrix 218
Latent vector of a polynomial matrix 218 256
Least common multiple of polynomials 212
Least upper bound norm 102 256 264
Left coprime polynomial matrices 219 256 270
Left divisibility of a polynomial matrix 218 256
Left divisor of a polynomial matrix 218 256
Left eigenvector of a matrix 256
Left inverse matrix 257
Left multiple of a polynomial matrix 218 257
Left quotient of polynomial matrices 218 257
Left remainder of polynomial matrices 218 257
Length of a vector 257 261
Leontief matrix 257
Leslie matrix 257
Liapunov matrix equation 258
Linear combination of matrices 258
Linear polynomial 212
Linearly dependent vectors 258
Linearly independent vectors 11 258
Loewner matrix 258
Lower block triangular matrix 258
Lower Hessenberg matrix 258
Lower triangular matrix 11 259 281
Lower triangular matrix, lub norm 102
Lower triangular matrix, properties of 164
M-matrix 259
Mahalanobis norm 103
Main diagonal of a matrix 259 268
Matrices, cogredient 233
Matrices, commuting 234
Matrices, conformable 236
Matrices, congruent 236
Matrices, conjunctive 236
Matrices, equivalent 243
Matrices, linear combination of 258
Matrices, orthogonally equivalent 265
Matrices, orthogonally similar 265
Matrices, permutation equivalent 266
Matrices, similar 216 275
Matrices, simultaneously diagonalizable 275
Matrices, unitarily equivalent 282
Matrices, unitarily similar 282
Matrix 1 259
Matrix decompositions 60 69
Matrix decompositions, block diagonal 90
Matrix decompositions, Choleski 86 92 154 155
Matrix decompositions, congruent canonical form 85 137
Matrix decompositions, diagonal 90
Matrix decompositions, diagonal reduction 60 85
Matrix decompositions, echelon form 88
Matrix decompositions, Gram — Schmidt 87 92
Matrix decompositions, Hermite canonical form 88
Matrix decompositions, Jordan 63 70 71 83 84 89
Matrix decompositions, of Hermitian matrix 137
Matrix decompositions, of positive definite matrix 154
Matrix decompositions, polar 61 88
Matrix decompositions, rank factorization 60 88
Matrix decompositions, Schur 69 86 92
Matrix decompositions, simultaneous diagonalization 86
Matrix decompositions, singular value 60 79 80 85 91
Matrix decompositions, spectral 69 70 85 90 137 163
Matrix decompositions, square root 155
Matrix decompositions, symmetric matrix 163
Matrix decompositions, triangular factorization 60 87
Matrix derivatives 171
Matrix difference 15
Matrix factorizations 60
Matrix function 259
Matrix multiplication 3 16 260
Matrix norm 101 260 262
Matrix norm, induced 108 252
Matrix norm, minimal 102
Matrix norm, properties of 106
Matrix norm, results for 106
Matrix norm, self-adjoint 102
Matrix operations 15
Matrix operations, elementary 242
Matrix polynomial 215 260
Matrix power series 215 260
Matrix product 3 16 260
Matrix sum 15
Matrix, absolute value of 225
Matrix, addition 225
Matrix, adjoint 225
Matrix, adjugate 226
Matrix, annihilating polynomial of 226
Matrix, antimetric 226
| Matrix, arithmetic 226
Matrix, band 227
Matrix, banded 227
Matrix, bidiagonal 227
Matrix, binary 227
Matrix, block 2 144 229
Matrix, block, band 227
Matrix, block, circulant 228
Matrix, block, companion 220 228
Matrix, block, diagonal 229
Matrix, block, Hankel 229
Matrix, block, Toeplitz 229
Matrix, block, triangular 230
Matrix, block, tridiagonal 230
Matrix, bordered 230
Matrix, bordered Gramian 230
Matrix, Brownian 230
Matrix, centro-Hermitian 231
Matrix, centro-symmetric 231
Matrix, characteristic 220 231
Matrix, characteristic determinant of 231
Matrix, characteristic equation of 231
Matrix, characteristic polynomial of 231
Matrix, characteristic root of 231
Matrix, characteristic value of 231
Matrix, characteristic vector of 232
Matrix, check 232
Matrix, circulant 113 232
Matrix, cofactor 232
Matrix, column dimension of 233
Matrix, column rank of 233
Matrix, column regular 233
Matrix, column stochastic 233
Matrix, column vectorization of 233
Matrix, commutation 9 31 115 123 127 234
Matrix, companion 213 234
Matrix, complex 1 235
Matrix, complex conjugate 235
Matrix, compound 235
Matrix, condition number of 236
Matrix, conditional inverse 236
Matrix, conjugate 236
Matrix, conjugate transpose 236
Matrix, controllability 236
Matrix, convergent 119 236
Matrix, cosine 236
Matrix, D-inverse 236
Matrix, decomposable 237 270
Matrix, defective 237
Matrix, deficient 237
Matrix, definite 237
Matrix, derivative 237
Matrix, derogatory 214 237
Matrix, determinant of 238
Matrix, diagonal 5 9 120 238
Matrix, diagonal dominant 238
Matrix, diagonal of 238
Matrix, diagonal similar 238
Matrix, diagonalizable 216 238
Matrix, dimension of 239 264
Matrix, dominating nonnegative 239
Matrix, doubly centered 239
Matrix, doubly quasi-stochastic 240
Matrix, doubly stochastic 139 240
Matrix, Drazin inverse 240
Matrix, duplication 9 31 51 53 118 122 127 130 149 157 165 240
Matrix, effective inverse 241
Matrix, eigenvalue of 241
Matrix, eigenvector 241
Matrix, eigenvector of 242
Matrix, elementary 242
Matrix, elimination 9 31 52 53 118 123 126 127 165 243
Matrix, EP- 243
Matrix, equality 243
Matrix, ergodic 243
Matrix, exchange 243
Matrix, exponential 244
Matrix, exponential function of 215 244
Matrix, flip 244
Matrix, foeplitz 114 279
Matrix, Fourier 114 244
Matrix, Frobenius 244
Matrix, g-circulant 245
Matrix, g-inverse 245
Matrix, generalized inverse 7 32 245
Matrix, generalized permutation 140 245
Matrix, geometric 246
Matrix, Givens 246
Matrix, gradient 246
Matrix, Gram 247
Matrix, gramian 247
Matrix, group inverse 247
Matrix, Hadamard 247
Matrix, Hamiltonian 248
Matrix, Hankel 249
Matrix, harmonic 249
Matrix, Helmert 249
Matrix, hermitian 10 131 250
Matrix, Hermitian adjoint 250
Matrix, Hessenberg 250
Matrix, Hessian 172 250
Matrix, Hilbert 251
Matrix, Hurwitz 214 251
Matrix, idempotent 10 138 251
Matrix, identity 2 10 252
Matrix, imaginary 252
Matrix, imprimitive 252
Matrix, indefinite 252
Matrix, index of 252
Matrix, inertia of 252
Matrix, integer 253
Matrix, integral 253
Matrix, inverse 7 27 253
Matrix, inverse, conditional 236
Matrix, inverse, Drazin 240
Matrix, inverse, effective 241
Matrix, inverse, g- 245
Matrix, inverse, generalized 245
Matrix, inverse, left 257
Matrix, inverse, Moore — Penrose 262
Matrix, inverse, MP- 262
Matrix, inverse, pseudo 269
Matrix, inverse, reflexive generalized 270
Matrix, inverse, right 271
Matrix, invertible 10 253 263
Matrix, involutory 254
Matrix, irreducible 254
Matrix, Jacobian 173 254
Matrix, Jordan 255
Matrix, Kronecker 255
Matrix, left inverse 257
Matrix, Leontief 257
Matrix, Leslie 257
Matrix, Loewner 258
Matrix, lower block triangular 258
Matrix, lower Hessenberg 258
Matrix, lower triangular 11 164 259
Matrix, M- 259
Matrix, main diagonal of 259
Matrix, Metzler 260
Matrix, minimal polynomial of 261
Matrix, Minkowski 261
Matrix, Minkowski — Metzler 261
Matrix, minor of 261
Matrix, minor of an element of 261
Matrix, modal 261
Matrix, monomial 261
Matrix, Moore — Penrose inverse 34 262
Matrix, multiplication 260
Matrix, multiplication by a scalar 262
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