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| Klein E. — Mathematical methods in theoretical economics |
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| Предметный указатель |
 th barycentric subdivision 130
 -open sets 59
 -net 62 66
Abelian group see "Commutative group"
Absolute value 22
Abstract systems 144
Accumulation points 50
Accumulation points, set of 52
Additive group 145
Adherence see "Closure of set"
Adherent point 52
Adjoint method of matrix inversion 257
Adjoint of matrix 254
Affine mapping 131
Aggregate demand function 120
Aggregate supply function 120
Alexandroff, P. 142 151 370
Algebra of sets 11
Algebraic complements 250 253
Algebraic structures 143—149 see
Allais, M. 370
Allen, R.G.D. 192 277 370
Annihilator 203
Anticommutative matrices 223
Antisymmetric relation 28
Apostol, T.M. 103 370
Arrow, K.J. 79 152 168 299 370 371
Associative laws 11
Associative operations 20
Attainable states 33 78
Attainable states, set of 33
Augmented matrix 266
Aumann, R. 168 371
Automorphism 145
Balanced growth mode 359
Barycenter 130
Barycentric coordinates 125
Barycentric coordinates, Brouwer's theorem and 136
Barycentric subdivision 129
Barycentric subdivision of complex 131
Barycentric subdivision of simplex 130
Basis of vector space 186
Begle, E.G. 142 371
Bellman's approximation theorem 289
Bellman, R. 228 299 311 312 317 357 371
Berge, C. 34 46 103 115 120 142 192 371
Bicompact sets 66
Bicompact sets, intersection of 69
Bicompact sets, open covering of 67
Bicompact sets, union of 69
Bicompactness 66—68
Bicompactness, countable compactness and 79
Bicompactness, sequential compactness and, in first countable spaces 79
Bicompactness, sequential compactness and, in general 63
Bicompactness, sequential compactness and, in metric spaces 69
Bidual space 203
Bijective mapping 7 85
Bilinear mappings 206
Binary relation 25—30
Birkhoff, G. 46 151 371
Block addition 213
Block multiplication 217
Block, H.D. 371
Bolzano theorem 95
Bordered Hessian 315
Boundary of set 58
Boundary point 58
Boundary set 57
Boundary simplex 125
Bounded function 102
Bounded set, definition 61
Bounded set, lower 61
Bounded set, totally 62 65
Bounded set, upper 61
Boundedness of sets 60—62
Bounding hyperplanes 323—333
Bounding hyperplanes, definition 324
Bourbaki, N. 79 120 371
Brouwer's theorem 136 350
Brouwer's Theorem, relation to Kakutani's Theorem 139
Brouwer, L.E.J. 371
Budget constraint 157
Cairns, S.S. 132 142 371
Canonical matrix see "Normal form of matrix"
Canonical matrix, column equivalent 236
Canonical matrix, row equivalent 236
Carrier simplex 132
Cartesian product see "Product of sets"
Cauchy sequence 78
Cayley — Hamilton theorem 285—287
Champernowne, D.G. 371
Characteristic equation 281
Characteristic polynomial 279—285
Characteristic roots see "Characteristic values"
Characteristic solution 274
Characteristic values 279—285
Characteristic values of real symmetric matrices 290
Characteristic vectors 279—285
Characteristic vectors, normalized 282
Charnes, A. 371
Chipman, J.S. 371
Circular relation 33
Closed cube 61
Closed half-spaces 323
Closed indifference curve see "Satiation consumption"
Closed intervals see "Intervals"
Closed multivalued function 119
Closed sets, definition of 55
Closed sets, intersection of 56
Closed sets, union of 56
Closed simplex see "Simplex closure
Closedness of sets 50—60
Closure of convex set 74
Closure of set 52
Coalition 167
Coalition, blocking 167
Cofactorm 249 252
Collection of sets see "Family of sets"
Column equivalent matrices 237
Column rank 230 see
Column space 231
Commodity 153
Commodity space 153
Common-point theorem 140
Commutative group 147
Commutative laws 11
Commutative matrices 223 311
Commutative operations 20
Commutative ring 148
Compactness 63—70
Compactness in  70
Compactness in first countable spaces 79
Compactness in metric spaces 69—70
Compactness, bi- 66
Compactness, countable 79
Complement laws 12
Complementary minors 250
Complementation of sets 10
Complete solution 274
Complete space 78
COMPLEX 127
Complex matrices 225 292
Complex numbers, set of 21
Complex, definition of 127
Complex, dimension of 128
Composite functions 87 113
Concave-contoured function 99
Conformable matrices 213
Congruence modulo m 133
Congruent matrices 303
| Conjugate bilinear function 177
Conjugate of vector 175
Conjugate symmetry 175
Connected sets 70
Connectedness 70—71
Consistent systems 226
Constrained quadratic forms 309—315
Consumer preferences 156
Consumers 157—161
consumption 24
Consumption plan 24
Consumption set 24 154
Consumption set, aggregate 78
Consumption set, assumptions 155
Continuity of multivalued function 109 112
Continuity of multivalued function, compactness and 113
Continuous mappings on compact sets 93—94
Continuous mappings on connected sets 95
Continuous mappings, multivalued 89—91
Continuous mappings, single-valued 109—113
Continuous preordering 156
Contour of function 98
Convergent sequence limit of 50
Convergent sequence of points 50
Convergent sequence of real numbers 50
Convergent subsequence 63
Convex closure 332
Convex combination 72
Convex cones 333—341
Convex hull see "Convex closure"
Convex hull of extreme points 322
Convex polyhedral set 333
Convex preordering 45
Convex set 72
Convex set, direct product of 72
Convex set, intersection of 73
Convexity of functions 96—100
Convexity of preorderings 45 166
Convexity of sets 72—74
Convex—contoured function 99
Cooper, W.W. 371
Core of economy see "Economy"
Correspondence see "Multivalued function"
Countable compactness 79
Countable compactness in first countable spaces 79
Countable compactness, bicompactness and 79
Countable compactness, sequential compactness and 79
Countable set 48
Countable set, union of 49
Covering 66
Covering of compact set 67
Covering of simplex boundary 130
Covering of totally bounded set 67
Covering, countable 79
Covering, finite 66
Covering, open 66
Cramer's rule 267 270
Debreu, G. 46 79 103 120 152 160 164 168 326 327 329 344 345 353 370 371 372
Decomposability of matrices 346—350 365—367
Decomposable square matrix 346
Demand correspondence 106
DeMorgan's laws 12
Dense in itself set 57
Dense set 57
Denumerable set 48
Dependent systems 349
Derived set 52
Determinant function 242—251
Determinant function, definition 243
Diagonal canonical form 303
Diagonal matrices 222 see
Diagonalizatio of real symmetric matrices 289
Diagonalization 287—293
Diagonalization theorem 288
Diameter of set 62
Dieudonne, J. 372
Difference of sets 9
Dimension of dual space 202
Dimension of vector space 187
Direct product of closed sets 56
Direct product of compact sets 65
Direct product of convex sets 72
Direct product of countable sets 49
Direct product of sets 18
Direct sum of vector subspaces 181 182
Disconnected sets 70
Disjoint sets 6
Distance between two vectors 178
Distance function see "Metric"
Distributive laws 12
Distributive operations 20
Dominant eigenvalue 352
Dorfman, R. 277 372
Dot product 175
Dual cone 336 338
dual operations 20
Dual space 200—203
Dual space, basis of 201
Dual space, definition 201
Duality in von Neumann model 365
Duality principle 12
Duality theorem 366
Dualization laws 12
Dunford, N. 34 79 103 168 372
Dynamic price adjustment 296
Dynamics of von Neumann model 361
Echelon matrices 235 237
Economic expansion 363
Economic expansion, existence theorem 363
Economic expansion, factor 363
Economy 33 167 327
Economy with continuum of agents 153
Economy with finite number of agents 153
Economy with infinitely many commodities 153
Economy, core of 167
Economy, decomposable 15
Economy, private-ownership 162
Economy, pure-exchange 167
Edgeworth, F. 168 372
Eigenvalues see "Characteristic values"
Eigenvector see "Characteristic vectors"
Eilenberg, S. 142 372
Elementary matrices 233
Elementary operations 232 264
Elementary operations, matrix inversion and 256
Empty simplex 125
Empty, null, or void set 4
Endomorphism 145
Equal sets 5
Equilibrium, definition 162
Equilibrium, existence theorem 165
Equilibrium, optimum and 328
Equivalence relation 30
Equivalence theorem 328
Equivalent sets 47
Equivalent systems 264—266
Equivalent systems, definition 265
Euclidean distance function see "Metric"
Euclidean metric space 25
Euclidean norm see "Norm of
Euclidean space 177
Excess demand 33 162
Excess demand, set 78
Excess demand, theorem 164
Existence of equilibrium see "Equilibrium"
Exterior of set 58
Exterior point 58
Extreme point 329
Faddeva, V. 228 372
Family of sets 6
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