Ben-Israel A., Greville T. — Generalized inverses: Theory and applications :: Электронная библиотека попечительского совета мехмата МГУ

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Ben-Israel A., Greville T. — Generalized inverses: Theory and applications

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Название: Generalized inverses: Theory and applications

Авторы: Ben-Israel A., Greville T.

Аннотация:

The field of generalized inverses has grown much since the appearance of the first edition in 1974, and is still growing. This book accounts for these developments while maintaining the informal and leisurely style of the first edition. New material has been added, including a chapter on applications, an appendix on the work of E.H. Moore, new exercises and applications.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 381

Добавлена в каталог: 03.06.2005

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Предметный указатель

norm      8 123
$\alpha$ - $\beta$ generalized inverse      118
$\alpha$ -approximate solution      119
$\lambda$ -vector      29
$\mathrm{EP}_r$ matrix      139
$\phi$ -metric projector      115
$\tilde Q\tilde R$ factorization      13 231 240
Absorbing chain      272
Absorbing state      272
Acute natrices      213
Acute perturbation      213
Adjoint      10
Admittance matrix      87
Affine set      162
Algebraic multiplicity      31
angle      7
Aperiodic state      272
B-singular value decomposition      224
B-singular values      224
B-SVD      224
Basic solution      107
Basic subspaces      210
Best rank-k approximation      189
Beta distribution      293
beta function      286
Bias      262
Binet — Cauchy formula      25
blue      255
Bott — Duffin inverse      79 85 131
Branches, currents      86
Canonical angles      207
Carrier      296
Cauchy — Schwartz inequality      6 124 209
Cauchy — Schwartz inequality, generalized      124
Cesaro average      274
Characteristic polynomial      30
Cholesky factorization      104
Cline's method      147 233
Closed set of states      272
Closure      295
Coefficient of inclination      205
Communicating states      271
Complementary subspaces      5
Compound matrix      28
Computation, basis for null space      21
Computation, basis for range space      21
Computation, Drazin inverse      146—149 232 233
Computation, full-rank factorization      22
Computation, group inverse      160 161 233
Computation, Hermite normal form      20 22
Computation, Moore — Penrose inverse      42 159 184 185 223 232—234 242 248
Computation, Smith normal form      33
Computation, {1,2,3}-inverse      41 159 231
Computation, {1,2,4}-inverse      41 159
Computation, {1,2}-inverse      39 40 158 185 229 230
Computation, {1,3}-inverse      185
Computation, {1,4}-inverse      185
Computation, {1}-inverse      36 185 230
Computation, {2}-inverse      43
Condition number      181
Consistent norms      16
Constrained inverse      79
Constrained least-square solution      94
Constrained minimum-norm least-square solution      99 227
Contraction      199
Convergent matrix      18
Convex body      123
Convex function      115
Convex set, rotund      125
Convex set, smooth      125
Coordinates, cylindrical      284
Coordinates, spherical      285
Covariance matrix      255
Cramer's rule      25 67 108 176 178
Current      86
Cylindrical coordinates      284
Decomposable      295
Density function      289
Derivative      269
Determinant      24
Difference equation, consistent initial solution      278
Difference equation, homogeneous      278
Difference equation, tractable      278
Differentiable      269
Dimension of inclination      205
Direct sum      295
Discriminant      81
Distance between subspaces      208
Distribution function      289
Distribution, $\chi^2$       293
Distribution, bivariate normal      293
Distribution, exponential      292
Distribution, spherical      292
Distribution, uniform      293
Domain      296
Drazin inverse      138 145 146
Drazin inverse, Cline's method      147 233
Drazin inverse, computation      146—149 232 233
Drazin inverse, limit form      149
Dual function      122
Dual norms      123
Dual set      123
Dual vectors      124
Eigenfunction      308
Eigenspace      11
Eigenvalue      11 308
Eigenvector      11
Electrical network      85 132
Electrical network, currents      85
Electrical network, dual transfer matrix      87
Electrical network, transfer matrix      87
Electrical network, voltages      85
Elementary matrices      18
Elementary operations      33
Elementary row operations      18
EP matrix      139
Equivalent matrices      15
Equivalent norms      8
Erdelyi g.i.      305
Ergodic chain      272
Ergodic state      272
Essentially strictly convex norm      115
Estimable function      255 259
Euclidean norm      6
Expected value      255
Extension      76
Extremal g.i.      320
Extremal solution      318
Factorization, $\tilde Q\tilde R$       13 231 240
Factorization, Cholesky      104
Factorization, full-rank      see Rank factorization
Factorization, QR      13 229 240
Fredholm integral operators      300
Frobenius covariants      54 57
Frobenius norm      16 97 189
Full-rank factorization      See Rank factorization
Function, convex      115
Function, strictly convex      115
Gamma function      286
Gauge function      122 204
Gauge function, symmetric      122
Gauss — Markov model      255
Gauss — Markov theorem      256
Gaussian elimination      20
Generalized Green's function      312
Generalized inverse      1
Generalized inverse, $\alpha$ - $\alpha$       118 130
Generalized inverse, $\{1^k,2,5\}$ -inverse      135
Generalized inverse, associated with $\alpha$ , $\beta$       118 130
Generalized inverse, constrained      79

Generalized inverse, Drazin inverse      138 145 146
Generalized inverse, maximal g.i.      303
Generalized inverse, Moore — Penrose inverse      159
Generalized inverse, quasi-commuting inverse      152
Generalized inverse, reverse order property      142 154
Generalized inverse, S'-inverse      149
Generalized inverse, S-inverse      144
Generalized inverse, S-restricted      77 98
Generalized inverse, strong spectral inverse      152
Generalized inverse, Tseng      300
Generalized inverse, {1,2,3}-inverse      40 159
Generalized inverse, {1,2,4}-inverse      40 159
Generalized inverse, {1,2,5}-inverse      138
Generalized inverse, {1,2}-inverse      39 158
Generalized inverse, {1,3}-inverse      91 97
Generalized inverse, {1,4}-inverse      97
Generalized inverse, {1}-inverse      37
Generalized inverse, {2}-inverse      264 265 269
Generalized inverse, {i,j,…,k}-inverse      35
Generalized power      222
Generalized resolvent      220
Geometric multiplicity      11
Grade      29
Gram matrix      25 67
Gram — Schmidt orthogonalization process      234
Gram — Schmidt orthonormalization process      7 13 24
Gramian      25
Graph      85 296
Graph nodes      85
Graph nodes, connected      86
Graph nodes, directly connected      86
Graph, branches      85
Graph, connected      86
Graph, incidence matrix      85
Green's function      311
Greville's method      234
Group inverse      138
Group inverse, computation      139 160 161 233
GSO      7 13 24 234
Hadamard inequality      26 209 210
Hermite normal form      20 22 36 230
Hermite normal form, computation      20 22
Idempotent      37 50
Ill-conditioned      92
Incidence matrix      85 87
Inclination, coefficient      205
Inclination, dimension      205
INDEX      136
Index of eigenvalue      31
Index of nilpotency      31 153
Inequality, Cauchy — Schwartz      6 124 209
Inequality, generalized Cauchy — Schwartz      124
Inequality, Hadamard      26 209 210
Inequality, Minkowski      8
Inequality, triangle      6
Inequality, Weyl      192
Inner product      5 295
Inner product, standard      6
Integral matrix      33 84
Integral vector      33 84
Interval linear program      82
Interval linear program, bounded      82
Interval linear program, consistent      82
Invariant factors      33
Inverse graph      296
Inverse, Bott — Duffin      79 85 131
Inverse, Drazin      146
Inverse, generalized      1
Inverse, Moore — Penrose      35 97 114 316
Inverse, weighted      105
Irreducible Markov chain      272
Irreducible matrix      34
Isometry      194
Isometry, linearity of      199
Isometry, partial      194 199
Iterative method      241
Iterative method, $p^{\underline{\mathrm{th}}}$ -order      241
Jacobian matrix      265 280
Jordan block      30
Jordan normal form      30 57 146 151
Kalman filter      294
Kirchhoff      86
Kirchhoff current law      86 132
Kirchhoff voltage law      86 132
Kronecker product      46
LE      255
Least extremal solution      318
Least upper bound      126
Least-squares solution, constrained      94
Least-squares solution, length      6
Least-squares solution, minimum-norm      96
Linear equations, approximate solution      91
Linear equations, ill-conditioned      92
Linear equations, least-squares solution      91
Linear estimator      255
Linear estimator, best unbiased      255
Linear estimator, unbiased      255
Linear manifold      162
Linear manifold, orthogonal representation      162
Linear operator, adjoint      297
Linear operator, bounded      296
Linear operator, carrier      296
Linear operator, closable      298
Linear operator, closed      296
Linear operator, closure      298
Linear operator, dense      297
Linear operator, domain      296
Linear operator, extension      297
Linear operator, graph      296
Linear operator, inverse graph      296
Linear operator, non-negative      298
Linear operator, normally solvable      298
Linear operator, null space      296
Linear operator, orthogonal projector      298
Linear operator, range      296
Linear operator, restriction      297
Linear operator, self-adjoint      298
Linear operator, symmetric      298
Linear regression      255
Linear statistical model      255
Linear statistical model, ridge regression estimator      262
Linear transformation      9
Linear transformation, extension      76
Linear transformation, intrinsic property      15
Linear transformation, inverse      9
Linear transformation, inverse image      9
Linear transformation, invertible      9
Linear transformation, matrix representation      9
Linear transformation, nonsingular      9
Linear transformation, null space      9
Linear transformation, range      9
Linear transformation, restriction      76
Loewner oredring      69
LUE      255
Markov chain      271
Markov chain, absorbing      272
Markov chain, closed set      272
Markov chain, ergodic      272
Markov chain, irreducible      272
Markov chain, recurrent      272
Markov chain, regular      272
Markov chain, state, absorbing      272
Markov chain, state, aperiodic      272
Markov chain, state, ergodic      272
Markov chain, state, leads      271
Markov chain, state, null      272
Markov chain, state, period      272
Markov chain, state, probabilities      273
Markov chain, state, recurrent      272
Markov chain, state, transient      272

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