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| Ben-Israel A., Greville T. — Generalized inverses: Theory and applications |
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| Предметный указатель |
Markov chain, states, communicate 271
Markov chain, stationary distribution 273
Matrices,  139
Matrices, convergent 18
Matrices, diagonable 52
Matrices, EP 139
Matrices, equivalent 15
Matrices, equivalent over Z 33
Matrices, idempotent 37 50
Matrices, ill-conditioned 92
Matrices, normal 65
Matrices, orthogonally similar 14
Matrices, positive definite 11 70
Matrices, positive semi-definite 11 70
Matrices, range-Hermitian 139
Matrices, similar 14
Matrices, unitarily equivalent 15
Matrices, unitarily similar 14
Matrix norm 11
Matrix norm, corresponding to a vector norm 17
Matrix norm, Frobenius 16 97 189
Matrix norm, multiplicative 11
Matrix norm, spectral 17 181
Matrix norm, unitarily invariant 17
Matrix norms, unitarily invariant 204
Matrix, admittance 87
Matrix, condition number 181
Matrix, function 58 217
Matrix, incidence 85 87
Matrix, index 136
Matrix, integral 33 84
Matrix, invariant factors 33
Matrix, irreducible 34
Matrix, nilpotent part 150
Matrix, nonnegative 33
Matrix, permutation 19
Matrix, perturbation 212
Matrix, polar decomposition 196
Matrix, reduced row — echelon form 20
Matrix, reducible 33
Matrix, set inclusion 88
Matrix, set intersection 88
Matrix, singular value decomposition, see SVD 13
Matrix, singular values 12
Matrix, square root 104 198
Matrix, stochastic 271
Matrix, transfer 87
Matrix, unit 33 84
Matrix, volume 25 27 107 177 187
Maximal g.i. 303
Mean square error 263
Minimal polynomial 31
Minimum-norm least-squares solution 96
Minimum-norm least-squares solution, constrained 99 227
Minimum-norm solution 94
Minkowski functional 122
Minkowski's inequality 8
Moore — Penrose inverse 35 97 114 159 185 316
Moore — Penrose inverse, computation 42 159 184 185 223 232—234 242 248
Moore — Penrose inverse, Greville's method 234
Moore — Penrose inverse, iterative methods 241
Moore — Penrose inverse, limit form 101 141
Moore — Penrose inverse, Noble's method 232
Moore — Penrose inverse, Schulz method 248
MSE — mean square error 263
Multiplicative norm 11
Multiplicity, algebraic 31
Multiplicity, geometric 11
N(S)-restricted pseudoinverse of T 323
Naive least-square estimator 259
Newton's method 264 265 269
Nilpotent 31
Nilpotent part 150
Noble's method 93 232 233
Nonnegative matrix 33
Norm 6 295
Norm of homogeneous transformation 126
Norm,  8 123
Norm, consistent 16
Norm, e.s.c. 115 129
Norm, ellipsoidal 7 127
Norm, equivalent 8
Norm, essentially strictly convex 115
Norm, Euclidean 6
Norm, matrix 11 17
Norm, projective 127
Norm, Tchebycheff 124
Norm, unitarily invariant 123
Norm, weighted Euclidean 7
Normal form, Hermite 20 22 36 230
Normal form, Jordan 30 57 146 151
Normal form, Smith 33 84
Normal matrix 65
Norms, dual 130
Null space 9 21 96 296
Null state 272
O.n. 7
O.n. basis 7
Ohm's law 86 132
Orthogonal 7
Orthogonal, complement 10 295
Orthogonal, direct sum 10 295
Orthogonal, projection 64
Orthogonal, projector 64
Orthogonal, Q 227
Orthogonally incident subspaces 205
Orthogonally similar matrices 14
Orthonormal 7. See also O.n.
Partial isometry 194 199
pd 11 70
Penrose equations 35 135 305 316
Period of state 272
Permutation matrix 19
Permutation, even 19
Permutation, inverse 19
Permutation, matrix 19
Permutation, odd 19
Permutation, sign 19
Perturbation 212
Perturbation, acute 213
Perturbation, operation 160
Perturbation, pivot 160
Pluecker coordinates 28 187 211
Polar decomposition 196
Polynomial, characteristic 30
Polynomial, minimal 31
Potential 81 86
Principal angles 207
Principal idempotents 54 57
| Principal vector of grade j 29
Projection 5
Projection, orthogonal 64
Projective, bound 126
Projective, norm 127
Projector,  -metric 115
Projector, orthogonal 64
PSD 11 70
Pseudo inverse 309
Pseudo resolvent 308
Pseudo resolvent, Hurwitz construction 308
Pseudoinverse 1
Q-orthogonal 227
QR factorization 13 229 240
Quasi-commuting inverse 152
Radon transform 282
RANGE 9 21 96 296
Range-Hermitian matrix 139
Rank factorization 22 27 28 42 44 51 64 76 101 106 109 139 147 159 187 231 233
Reciprocal subspaces 205
Reciprocal vectors 205
Recurrent chain 272
Recurrent state 272
Reduced row-echelon form 20
Reducible matrix 33
Regular chain 272
Regular value 308
Residual 91 240 241
Resolvent 60 220
Resolvent, equation 60 220
Resolvent, generalized 220
Restriction 76
Reverse order property 142 154
Ridge regression estimator 262
Rotund convex set 125
RRE — ridge regression estimator 262
S'-inverse 149
S-inverse 144
S-restricted {1,3}-inverse 98
S-restricted {1,4}-inverse 98
S-restricted {i,j,…,k}-inverse 77
Schmidt approximation theorem 189 192
Schulz method 248
Schur complement 26 34 159 178
Set inclusion matrix 88
Set intersection matrix 88
Similar matrices 14
Singular value decomposition, see SVD 13
Singular values 12
Singular values, B 224
Singular values, generalized 224 227
Singular values, {W,Q} 227
Smith normal form 33 84
Smooth convex set 125
Solution,  -approximate 119
Solution, approximate 91
Solution, basic 107
Solution, least-squares 91
Solution, minimum-norm 94
Solution, Tchebycheff 124
Spectral condition number 182
Spectral decomposition 54 57 71 104
Spectral norm 17 181
Spectral radius 17
Spectrum 11 58
Spherical coordinates 285
Spline approximation 329
Square root of a matrix 198
Square root of a matrix, inner product 6
Square root of a matrix, standard basis 5
Standard basis 10
Star order 73
Stationary distribution 273
Stationary point 132
Stationary value 132
Stochastic matrix 271
Strictly convex function 115
Strong spectral inverse 152
Subspaces, orthogonally incident 205
Subspaces, reciprocal 205
Subspaces, totally inclined 205
SVD 13 179 183 185—187 229 262
SVD, history 185
Tchebycheff, approximate solution 124
Tchebycheff, norm 8 124
Tihonov regularization 100
TLS 190
Total least squares 190
Totally inclined subspaces 205
Transient state 272
TREE 88
Triangle inequality 6
Tseng generalized inverse 300
UDV*-decomposition 186
Unit matrix 33 84
Unitarily equivalent matrices 15 180 199
Unitarily invariant matrix norms 204
Unitarily invariant norm 17 123
Unitarily similar matrices 14
Vector integral 33 84
Vector length 6
Vector norm 6 123
Vector principal 29
Vectors, reciprocal 205
Volume 25 27 107 177 187
Volume, k-volume 29
Wedderburn decomposition 149 151
Weighted inverse 105
Weighted least squares 109
Weighted {1,2}-inverse 104 105 228
Weyl inequalities 192
{1,2,3}-inverse 40
{1,2,3}-inverse, computation 41 159 231
{1,2,4}-inverse 40
{1,2,4}-inverse, computation 41 159
{1,2}-inverse 39 185
{1,2}-inverse, computation 39 40 158 185 229 230
{1,2}-inverse, weighted 104 105 228
{1,3}-inverse 91 97 185
{1,3}-inverse, computation 185
{1,4}-inverse 97 185
{1,4}-inverse, computation 185
{1}-inverse 35 37 185
{1}-inverse, computation 36 185 230 231
{2}-inverse 264 265 269
{2}-inverse, computation 43
{i,j,…,k}-inverse 35
{W,Q}-singular values 227
{W,Q}-weighted {1,2}-inverse 104 105 228
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