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Klein E. — Mathematical methods in theoretical economics
Klein E. — Mathematical methods in theoretical economics

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Название: Mathematical methods in theoretical economics

Автор: Klein E.

Аннотация:

Topological and vector space methods have achieved a very distinguished position among the tools of theoretical economics, especially in the area of equilibrium analysis. This book aims at giving a systematic presentation of the basic principles of these two areas of mathematics. With'this aim in mind, we hope the book may prove to be a useful introduction to the field for students of theoretical economics as well as a reference work for economists interested in these problems.
A year of calculus and a semester of elementary linear algebra should provide the reader with the mathematical background needed to understand this book. Some familiarity with modern algebra and differential equations is desirable though not necessary. Finally, it is assumed that the reader has already had some serious exposure to modern mathematical economics at the graduate level.
The book consists of two parts, each of which is essentially self-contained.
Read more at http://ebookee.org/Mathematical-Methods-in-Theoretical-Economics-Topological-and-Vector-Space-Foundations-of-Equilibrium-Analysis_1104691.html#YyPOZIJQkdwEAttv.99


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 408

Добавлена в каталог: 22.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\nu$th barycentric subdivision      130
$\tau$-open sets      59
$\varepsilon$-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 $E^{n}$      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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