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| Авторизация |
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| Campbell S.L., Meyer C.D. — Generalized Inverses of Linear Transformations (Classics in Applied Mathematics) |
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| Предметный указатель |
 matrices 109 118
Absorbing, chain 152 165 169
Absorbing, state 152
Absorbtion probability 166
Adjoining a row and/or a column 54
Algorithms 260
Analytic matrix valued function 227
Backward population projection 184
Best linear unbiased estimate 109
Block, form 3
Block, triangular matrix 61
blue 109 112 113 114
Bott — Duffin inverse 117
Calculation of the Moore — Penrose inverse 247
Canonical form for the Drazin inverse 122
Cauchy's inequality 234
Characteristic polynomial 132 207
Closest vector 29
Coefficient of determination 35
Common solution 98
Commutator-[X, Y] 23
Commuting weak Drazin inverse 203
Complementary subspace 3
Component matrices 201
Computation of the Drazin inverse 255
Computational concerns 246
Condition number 224 247
Conformable 53
Conjugate transpose 2
Consistent, initial vector 172 182
Consistent, model 106
Consistent, norms 212
Consistent, systems 93
Constrained, generalized inverse 68
Constrained, least squares solutions 65
Constrained, minimization 63
Continuity of generalized inverses 210
Continuity of the Drazin inverse 232
Continuity of the index 233
Continuity of the Moore — Penrose inverse 216
Core of a matrix 127
Core-nilpotent decomposition 128
Curve fitting 39
Cyclic chain 152
Deflation 258
Derivative of matrix valued function 226
Derivative of Moore — Penrose inverse 227
Design matrix 32
Difference equations-systems 181
Differential equations-systems 171
Direct sum 3
Directed graph 117
Discrete control problem 197
Distinguished columns 15
Doubly stochastic matrix 163
Drazin inverse as a limit 136
Drazin inverse of a partitioned matrix 139
Drazin inverse, a polynomial 130
Drazin inverse, algebraic definition 122
Drazin inverse, functional definition 122
Dual 238
Electrical engineering 77
EP, matrices 208
EP, matrix 74 129
Equation solving inverses 93
Equivalent norms 212
Ergodic, chain 152 158
Ergodic, set 151 166
Ergodic, state 151 165
Estimable 106
Estimating equation 34
Euclidean norm 28
Expected, absorption times 169
Expected, number of times in a state 158
Farkas Theorem 239
Feasible solution 238
Final space 72
Finite Markov chain 151
Fitting a linear combination of functions 43
Fixed probability vector 156 160 162 208
Flat 31
Full rank factorization 14 15 16 148 149 249
Functional, error 30
Functional, relationship 30
Functions of a matrix 200
Fundamental matrix of constrained minimization 63
Gauss — Markov theorem 105
Gaussian elimination 246 250
General solution of AXB = C 97
Generalized, eigenvector of grade P 129
Generalized, inverse of a sum 46
Generalized, inverse, functional definition 8
Generalized, inverse, Moore definition 9
Generalized, inverse, Newton method 118
Generalized, inverse, Penrose definition 9
Givens rotation 249 252
Goodness of fit 34 38 39
Group inverse 124
Group inverse of a block triangular matrix 143
Hermite, echelon form 15
Hermite, form 115 117
Hermitian 2
Homogeneous, Markov chain 151
Homogeneous, systems-differential equations 175
Householder transformation 249 251
Idempotent matrices 201
Impedance 78
Impedance, matrix 80
Inconsistent systems 94
Index of a block triangular matrix 142
Index of a matrix 121 138
Index of a product 150
Index of zero eigenvalue 132
Initial, space 72
Initial, value problem 172
Inputs 78
Integer solution 116
Integration of exponential 176
Intercept hypothesis 32
Invariant subspace 4 7
Inverse function 8
Inverse-(1) 96
Inverse-(1, 2) 96
| Inverse-(1, 2, 3, 4) 96
Inverse-(1, 3) 96
Inverse-(1, 3, 4) 25
Inverse-(1, 4) 96
Inverse-(i, j, k) 91 95
Isometry 71
Iterative methods 250 261 262
Kirchhoff law 78
Kronecker product 115
Least, squares generalized inverse 95
Least, squares solution 28
Leslie, matrix 185
Leslie, population model 184
Limited probability 168
Limits for transition matrices 155
Linear, estimation 104
Linear, functional relationship 30
Linear, hypothesis 30
Linear, model 105
Linear, programming 237
Linear, unbiased estimates 107
Linearly unbiased estimate 106
Markov process 151
Matrix, norm 211
Matrix, valued functions 224
Maximal element 127
Mean first passage matrix 159
Measurable matrix valued functions 235
Measurement errors 30
Meromorphic matrix valued function 228
Minimal, least squares solution 28
Minimal, norm constrained least squares solutions 67
Minimal, polynomial 132 207
Minimal, rank weak Drazin inverse 203
Minimal, V-norm solution 117
Minimal, V-seminorm W-least squares solution 118
Minimum, norm generalized inverse 94
Minimum, variance linear unbiased estimate 107
Modified matrices 51
Moore — Penrose inverse 10 92
Moore — Penrose inverse as an integral 26
Moore — Penrose inverse of block triangular matrix 62
Moore — Penrose inverse of partitioned matrix 54 55 58
Moore — Penrose inverse of rank 1 matrix 25
n-port network 78
Nilpotent part of a matrix 128
No intercept hypothesis 32
Nonlinear least squares 229
Norm, matrix 211
Norm, operator 211
Norm, vector 210
normal 5
Normal, equations 29
NR-Generalized inverse 92
Null space 2
Oblique projector 92
Operation 52
Operator norm 211
Optimal, control 187 189
Optimal, value 239
Optimal, vector 238
Orthogonal projector 2 3 29 92 218
Outputs 78
p-Norm 211
Parallel sum 82 84
Partial isometry 72
Partitioned, matrices 116
Partitioned, matrices, (1)-inverse 98
Partitioned, matrices, (1, 2)-inverse 100
Partitioned, matrix 53
Perturbation of the Moore — Penrose inverse 224
Polar form 5 73
Polyhedral cone 244
Port 78
Positive semi-definite 102
Prescribed range null space inverse 92 93
Product moment correlation 35
Projective weak Drazin inverse 203
Projector 2
Proper splitting 262
Properly partitioned block triangular matrix 61
Property of homogeneity 78
Property of superposition 78
Pyle's formulation 241
Qudratic cost functional 188
RANGE 2
Rank 1 modification 47 116
Rank of block triangular matrix 104
Rank of partitioned matrix 102
Rank, function 225
Reciprocal network 81
Rectangular systems of differential eq 178
Reducing subspace 4 7
Regular chain 152 157
Relative error 34
Resistive network 82
Restricted, linear model 115
Restricted, linear transformation 9 91 121
Restricted, model 106
Reverse order law 19 26 95 115 149
Row, echelon form 14
Row, space 101
Shorted, matrices 86
Shorted, matrix 87
Singular value 6 214
Singular value, decomposition 6 247 251
Slack variables 237
Special, mapping property 75 205
Special, properties of the Drazin inverse 129
Standard basis 47
Star cancellation law 3
Stochastic matrix 152
Sup norm 211
Terminals 77
Tractable 172 182
Transient set 151 165 168
Transition matrix 151
Unitary matrices 12 72
Variance of first passage time 160
Weak Drazin inverses 202 203
Weighted, generalized inverse 117
Weighted, least squares solution 117
Weighted, Moore — Penrose inverse 118
Weighted, normal equations 115
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