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| Klein E. — Mathematical methods in theoretical economics |
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| Предметный указатель |
Fan, K. 372
Fang, J. 151 372
Feasible consumption 105
Field 148
Field, matrix over 272
Field, vector space over 172
Finite convex cone 337
Finite covering 66
Finite set 4 48
Finite simplicial complex see "Complex"
Finkbeiner, D.T. 192 262 243 372
Finsler's theorem 311
First element of set 39
First minor see "Minor"
Fixed point 121—123
Fixed point of multivalued functions 137—140
Fixed point of single-valued functions 123 135—137
Fixed point, definition 121
Fraenkel, A. 16 372
Franz, W. 34 79 142 372
Frechet, M. 372
Frobenius root see "Dominant eigenvalue"
Frobenius theorem 350
Frobenius, G. 372
Function 6
Function, definition 6 81 105
Function, multivalued 104—120
Function, set- 102
Function, single-valued 81—103
Fundamental theorem of algebra 281
Gale, D. 152 168 199 277 320 321 322 362 363 366 369 372
Gantmacher, F.R. 192 228 241 299 317 357 373
General equilibrium 152—166
General equivalence 237
Generators of cone 337
Goldberger, A. 373
Greatest lower bound (glb) 43
Group isomorphism 147
groups 145—147
Groups, additive 145
Groups, commutative 147
Groups, isomorphic 147
Groups, multiplicative 146
Hadley, G. 192 262 277 373
Hahn, F. 168 299 371
Hahn, W. 299 373
Halanay, A. 299 373
Half-line 333
Half-spaces 323 333
Hall, D.W. 373
Halmos, P. 16 192 373
Hausdorff, F. 16 373
Hawkins — Simon theorem 276 299 373
Henderson, A. 371
Hermitian matrices 225
Herstein, I. 46 103 353 372 373
hessian 315
Hicks, J.R. 373
Hildenbrand, W. 168 373
Homeomorphic spaces 92
Homeomorphism 92
Homogeneous linear systems 271
Homomorphism 144
Homomorphism, vector space 189—190 193—206
Hopf, H. 142 370
Howe, C.W. 369 373
Hurewicz, W. 373
Hurwicz, L. 299 371
Hyperplane 323
Idempotent laws 11
Idempotent matrices 223
Identification of linear systems 265
Identity elements 21
Identity laws 12
Identity matrix 221
Identity transformation 195
Increasing functions 92
Indecomposability and duality 365—367
Indecomposable rectangular system 366
Indecomposable square matrix 346
Indecomposable von Neumann model 365
Indefinite form 302
Independent subeconomy 227
Independent subsystems 348
Index set see "Family of sets"
indexed 8
Indirect utility function see "Utility function"
Infimum 43
Infimum, uniqueness of 43
Infinite sequence 48
Infinite set 4 48
Initial resources 158
Injective mapping 84
Inner product see "Dot product"
Inner product function 177
Inner product space 177
Input-output system 227 270 273 319 355
Input-output table 15
Integers set of 21
Integral domain 148
Intensity level 360
Interior equilibrium 358
Interior of set 58
Interior point 58
Intermediate-value theorem 95
Intersection 8
Intersection of bicompact sets 69
Intersection of closed sets 56
Intersection of convex cones 335
Intersection of convex sets 73
Intersection of open sets 56
Intersection of sequentially compact sets 68
Intersection of vector subspaces 181
Intervals 22
Intervals, properties of 22—23
Into function see "Injective mapping"
Intriligator, M.D. 317 373
Inverse elements 21
Inverse matrix 221
Inverse point-to-point mapping 108
Inverse relation 27
Inverse transformation 195 198—200
Irrational numbers set of 21
Isolated point 51
Isomorphic groups 147
Isomorphism 145
Kakutani's theorem 138 164
Kakutani's theorem, relation to Brouwer's theorem 139
Kakutani, S. 142 373
Karlin, S. 103 168 277 299 357 369 373
Kelley, J.L. 79 373
Kemeny, J.G. 16 369 374
Kernel of group homorphism 151
Kernel of linear transformation 196
Keynesian system 208
Knaster — Kuratowski — Mazurkiewicz theorem 135 374
Knaster, B. 374
Koopmans, T.C. 16 277 344 374
Krein — Milman theorem 322 329—333
Kronecker delta 201
Kuhn, H.W. 374
Kuratowski, K. 34 46 79 103 142 374
Lancaster, K. 192 277 312 313 317 357 374
Lang, S. 326 356 374
Lange, O. 277 344 374
Laplace expansion 253
largest element see "Last element of set"
Last element of set 39
Least upper bound (lub) 43
Lebesgue lemma 135
| Lebesgue number 135 136
Lefschetz, S. 374
Length of vector see "Norm of vector"
Leontief economy see "Input-output system"
Leontief, W.W. 277 374
Lexicographic ordering 44
Limit point of sequence 50
Limit point of set 51
Linear algebras 205—206
Linear algebras, definition 205
Linear combination of vectors 180
Linear economic theory 340 see
Linear equations system, general theory see "Linear systems"
Linear equations system, nonnegative solutions of 320
Linear functional 200—203
Linear functional, definition 201
Linear functions see "Linear transformations" "Vector-space
Linear functions, convex sets and 101 118
Linear functions, multivalued 118
Linear functions, single-valued 100—101
Linear inequality systems 319—323
Linear inequality systems, nonnegative solutions of 321
Linear manifold 323 324
Linear multivalued function see "Linear functions"
Linear programming 330
Linear subspace 333
Linear systems 266—274 see
Linear systems, characteristic solution of 274
Linear systems, complete solution of 274
Linear systems, fundamental theorem on 274
Linear systems, particular solution of 274
Linear transformations 193—195 see "Vector-space
Linear transformations, composite 194 199
Linear transformations, definition 194
Linear transformations, operations with 194
Linear transformations, special 195 198—200 204
Linear transformations, transpose 204
Linearly independent points in  124 183
Linearly independent set of vectors 183—186
Lipschutz, S. 79 374
Local stability 297
Lower bounded set 61
Lower bounds of intervals 22
Lower bounds of sets 42
Lower bounds, set of 43
Lower semicontinuity of multivalued functions 111—112
Lower semicontinuity of single-valued functions 114—115
Lower triangular matrices see "Triangular matrices"
MacLane, S. 151 371
Mappings, point-to-point 80—103
Mappings, point-to-set 104—120
Mappings, set properties and 92—96 113
Market equilibrium 33
Matrices and linear transformations 209—211
Matrices definition 212
Matrices of functions 293—297
Matrices, operations with 212—213
Matrices, special matrices 218 221
Matrices, transpose 218
Matrix  352
Matrix equivalence 232—239
Matrix exponential 295 297
Matrix inversion 255—259
Matrix multiplier 295
Matrix operations 212—217
Matrix similarity 239
Matrix-valued functions 293 294
Maximal eigenvalue 352
Maximal element 328
Maximal element of set 39
Maximal independent set of vectors 185
Maximizer 94
Maximum 94
Mazurkiewicz, S. 374
McKenzie, L. 152 168 374
Mendelson, B. 16 34 374
Metric in vector space 176—179
Metric spaces 24—25
Metric spaces, definition 25
Metric, absolute value 25
Metric, definition of 24
Metric, Euclidean 25
Milnor, J. 46 103 373
Minimal element of set 39
Minimizer 94
Minimum 94
Minkowski's theorem 324—329
Minor 249
Mirkill, H. 374
Montgomery, D. 142 372
Morgenstern, O. 344 374
Morishima, M. 168 277 299 369 374
Multiplicative group 146
Multisectoral economic model 350
Multivalued function 105—109
Multivalued function, definition 105
Multivalued function, domain and range 106
Multivalued function, graph of 107
Multivalued transformation see "Multivalued function"
Murata, Y. 357 374
Natural numbers see "Positive integers"
Negative definite form 302
Negative definite matrix 307—308
Negative semidefinite form 302
Negative semidefinite matrix 307—308
Neoclassical demand theory 314
Neoclassical production functions 100
Nested principal minors see Principal minors
Net demand 33
Nikaido, H. 79 103 120 152 168 192 277 299 344 357 369 375
Nilpotent matrices 223
Nonantisymmetric relation 28
Nonhomogeneous linear systems 226
Nonnegative decomposable matrices 351—352
Nonnegative definite form 302
Nonnegative definite matrix 306
Nonnegative indecomposable matrix 350—351
Nonnegative matrix 346
Nonnegativity constraints 346
Nonpositive definite form 302
Nonpositive definite matrix 308
Nonsingular forms 301
Nonsingular linear transformation 198—200
Nonsingular matrix 221
Nonsymmetric relation 28
Norm of point 61
Norm of vector 178
Normal form of matrix 237
Normal vectors 179
Null space of a transformation see "Kernel"
Nullity of a linear transformation 196
n—dimensional simplex 124 see
One-to-one function 7 see
Onto function see "Surjective mapping"
Onto—into function see "Bijective mapping"
Open covering 66
Open intervals see "Intervals"
Open sets of topology 59
Open sets, definition 55
Open sets, intersection of 56
Open sets, union of 56
Open simplex 124
Operations 19—21
Operations on comparable sets 11
Operations with sets 8
Operations, binary 19
Operations, n-ary 19
Optimum and equilibrium 328
Ordered set, partially 37
Ordered set, totally 37
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