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Bapat R.B., Raghavan T.E.S. — Nonnegative Matrices and Applications
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Название: Nonnegative Matrices and ApplicationsАвторы: Bapat R.B., Raghavan T.E.S. Аннотация: This book presents an integrated treatment of the theory of nonnegative matrices, emphasizing connections with the themes of game theory, combinatorics, inequalities, optimization, and mathematical economics. Some related classes of positive matrices such as positive semidefinite matrices, M-matrices, P-matrices, and distance matrices are also discussed, but the main emphasis is on entrywise nonnegative matrices. The book begins with the basics of the subject, such as the Perron-Frobenius Theorem. Only a minimal background in linear algebra is assumed, although familiarity with linear programming and statistics will be helpful in following some sections. Each of the later chapters is devoted to an area of applications, including doubly stochastic matrices (price fixing, scheduling, and the fair division problem), combinatorial matroids, and economics. These applications have been carefully chosen both for their elegant mathematical content and for their accessibility. The treatment is rigorous and almost all results are proved completely. About half of the material in the book presents standard topics in a novel fashion, the remaining portion reports many new results in matrix theory for the first time in a book form.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 336Добавлена в каталог: 07.12.2005Операции: Положить на полку |
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118 294 Absorbing 48 Accessible 47 Achilles, E. 260 315 Adjacency matrix 209 Afriat, S.N. 134 315 Agresti, A. 272 315 Alexandroff inequality 92 188 189 195 196 203 236 238 Alexandroff inequality for mixed discriminant 203 Alexandroff, A.D. 93 315 Alexandroff, P. 24 315 Algebraic multiplicity 5 215 Analytic function 24 Anderson, W.N.Jr. 153 156 158 160 315 Ando, T. 144 153 158 315 Aperiodic 48 Apostol, T.M. 302 315 Arithmetic mean-geometric mean inequality 80 127 137 156 268 Arrow, K.J. 311 312 315 Assignment game 96 Associated with a matrix 4 236 Average weight 220 Baccelli, F.L. 225 315 Bacharach, M. 246 310 315 Balancing algorithm 262 Bapat, R.B. 56 72 83 117 121 144 148 153 156 158 184 189 193 203 209 218 225 235 238 246 250 290 316 317 321 Barndorff-Neilson, O.E. 272 317 Bartlett, M.S. 266 317 Base 207 Basic class of an isolated block 38 Bass, H. 311 317 Bauer, F.L. 260 317 Baum, L.E. 88 317 Baumol, W.J. 246 325 Baxter, B.J.C. 177 317 Bazarra, M.S. 64 273 317 Bellman, R. 173 317 Ben-Israel, A. 238 316 Benson, C.T. 218 320 Berman, A. 25 235 317 Bernstein's theorem 176 Bhaskara Rao, K.P.S. 234 325 Bhatia, R. 111 317 Bhattacharyya, T. 111 317 Biggs, N. 197 209 317 Binomial distribution 185 Birkhoff von-Neumann Theorem 59 63 64 67 71 76 82 97 106 107 111 126 Birkhoff, G. 63 64 66 68 73 75 76 82 105 107 111 126 150 203 239 251 255 257 260 317 Bishop, Y.M.M. 272 317 Bisubmodularity 112 Blackwell, D. 24 317 Blair, P.D. 275 323 Blumenthal, L.M. 164 165 317 Bondareva — Shapley Theorem 95 Bondareva, O.N. 95 103 317 Bondy, J.A. 4 105 197 317 Boolean algebra 225 Boolean matrix 225 Bozejko, M. 190 318 Braker, J.G. 225 318 Brauer, A. 44 318 Bregman, L.M. 44 88 273 318 Brouwer's fixed point theorem 5 53 184 272 Brown, D.T. 246 318 Brualdi, R.A. 64 72 105 184 246 318 Budget allocation problem 239 Burago, Y.D. 93 209 318 Busemann, H. 260 318 Bushell, P.J. 260 318 c.n.d. matrix 161 c.p.d. matrix 161 Cao, Z.-Q. 234 318 Caratheodory's theorem 56 64 111 Carre, B. 225 318 Cartan matrix 214 Cauchy — Binet formula 235 Cauchy — Schwarz inequality 147 180 235 Chaiken, S. 236 318 Chainable entries 67 Champernowne, D.G. 290 318 Characteristic function 94 Chetty, C.S.K. 194 325 Chvatal, V. 21 75 241 318 Circuit 220 Circuit geometric mean 130 Circuit matrix 124 Circuit mean 220 Circuit product 130 class 38 Closed system 287 Coalition 94 Coefficients of production 278 Cohen's theorem 134 Cohen, G. 225 316 318 Cohen, J.E. 133 134 318 Communicating states 47 Complementary slackness 32 250 281 282 289 310 Completely mixed game 10 Completely mixed strategy 10 Completely monotonic function 176 Completely reducible matrix 125 Comtet, L. 190 318 Conditionally negative definite matrix 161 Conditionally positive definite function 186 Conditionally positive definite matrix 161 Cone 4 51 58 Connell, E.H. 311 317 Constant returns to scale 278 Constantine, G.M. 209 316 318 Contingency table 243 Contracting model 288 Contraction mapping theorem 259 Contraction ratio of Birkhoff 255 Convex 4 Convex cone 251 Convex function 165 Convex set 4 5 53 59 60 98 165 166 193 293 Cooperative game 94 Core 94 Cottle, R.W. 30 172 179 319 Coxeter graph 213 Coxeter group 213 Coxeter, H.S.M. 218 319 Csima, J. 105 318 Cuninghame-Green, R.A. 225 319 Curiel, I. 105 319 Cvetkovic, D.M. 219 319 Cyclic matrix 40 Darroch, J.N. 267 319 Deming, W.E. 246 319 Deodhar, V.V. 218 319 Dependent set 197 Descarte's rule of signs 194 Deutsch, E. 134 319 Deviation balancing algorithm 263 Deviation reduction algorithm 262 Dey, A. 156 319 Dharmadhikari, S. 194 319 Diagonal product 61 80 87 Diagonalizable 215 Diagonally dominant matrix 296 Diameter 255 Direct sum of matroids 209 Directed graph 4 56 220 223 Discrete distributions 185 Distance matrix 164 Doob, M. 219 319 Doubly stochastic matrix 59 63—65 69 75 83 87 88 96 106 111 124 127 149 152 158 159 180 187 202 244 261 263 273 Doubly stochastic pattern 57 82 118 244 261 Dual 51 285 Duality theorem 22 30 32 33 74 89 95 238 250 Dubois, D. 225 318 Dudnikov, P.I. 225 319 Duff, I.S. 246 319 Duffin, R.J. 156 315 Dulmage, A.L. 64 321 Dwyer, P.S. 246 319 Eagon, J.A. 88 317 Eaves, B.C. 130 319 Economic expansion rate 288 289 Egorychev, G.P. 59 88 93 203 319 Eigenpair 221 Eigenvalue over max algebra 220 Electrical networks 153 Elementary symmetric function 156 Elsner, L. 111 124 134 158 319 entropy 185 Erisman, A.M. 246 319 Expanding model 288 EXPONENT 218 Extreme point 60 Factor of production 277 Factor price equalization 290 Fair division problem 108 Falikman, D.I. 59 88 93 203 319 Fan, K. 28 311 319 Farkas' Lemma 22 Feasible solution 22 Feinberg, S.E. 272 318 320 Feller, W. 51 246 319 Ferland, J.A. 172 179 319 320 Fibonacci sequence 116 Fiedler's Inequality 137 142 Fiedler, M. 28 121 144 311 320 Final class of an isolated block 38 Finite vector 220 Fischer Inequality 137 Fisher, M.E. 314 320 Flam, H. 276 320 Flanders, M.J. 276 320 For positive definite matrices 156 Franklin, J. 250 260 320 Friedland, S. 134 160 320 Friedlander, D. 243 320 Frobenius norm 111 Frobenius normal form 38 47 237 238 Frobenius — Koenig theorem 62 108 199 201 Frobenius, G. 1 4 15—17 23 24 34 38 43 44 47 54 57 115 199 201 216 219 236 251 260 275 278 284 285 309 310 320 Fuller, A.T. 314 320 Fully indecomposable matrix 66 Fundamental theorem of natural selection 121 Gale — Nikaido Theorem 305 312 Gale, D. 21 103 290 304 310 311 320 Gantmacher, F.R. 24 215 320 Gaubert, S. 225 320 Gaussian elimination 30 241 Generalized inverse 229 Generalized log-concave function 186 Generic matrix 70 Geometric multiplicity 5 215 Globally univalent map 292 Gokhale, D.V. 272 320 Golden ratio 116 Gondran, M. 225 320 Gonzales, T. 105 320 Graph 197 209 219 236 Graphic 197 Gravity model 245 Gregory, D.A. 234 320 Grove, L.C. 218 320 Haberman, S.J. 270 272 321 Hadamard inequality 134 136 144 Hadamard product 41 Hadamard — Fischer inequality 140 Hadamard, J. 115 134 136—138 140 141 144 148 159 321 Hall's theorem 199 Hall, P. 62 321 Hande, S.N. 156 319 Hardy — Littlewood — Polya Theorem 149 Hardy, G.H. 80 149 204 321 Hartfiel, D.J. 72 112 321 Heckscher, E. 310 311 321 Heilman, O.J. 236 321 Herstein, I.N. 21 321 Hicks, J.R. 276 306 312 321 Hicksian stable 307 Hide-and-seek problem 75 Hilbert's projective metric 254 Hobby, C. 88 273 321 Hoffman — Wielandt Theorem 111 Hoffman, A.J. 111 130 319 321 Holladay, J.C. 41 51 321 Holland, P.W. 272 317 Hopf, E. 260 321 Hopf, H. 24 315 Horn, R. 117 121 321 Horwich, G. 312 321 Hotelling, H. 246 321 Householder, A.S. 24 321 Howlett, R.B. 219 321 Humphreys, J.E. 218 321 Hungarian method 75 Hurwicz, L. 312 315 Hypergeometric distribution 195 Idempotent matrix 229 Immanant 148 Imperfectly stable market 306 Inada, K. 311 312 321 Incidence matrix 198 Income effect 306 Independent set 197 Index of 41 Index of a graph 210 Index of primitivity 41 Infinite vector 220 Information Inequality 80 118 268 Interpolation problem 173 Inventory model 45 inversion 189 Irreducible 46 Irreducible matrix 2 Isolated block 38 Iterative methods 28 Jacobi formula 140 Jacobian conjecture 304 311 312 Jacobian matrix 302 Jain, S.K. 234 316 Jentzsch, R. 260 321 Joag-Dev, K. 194 319 Johnson, C.R. 117 121 124 144 148 158 319—321 Johnson, D.M. 64 321 Kaneko, M. 310 322 Kaplansky's Theorem 11 Kaplansky, I. 11 15 322 Karlin 21 24 134 160 189 303 322 Keller, O. 303 322 Kelly, P.J. 260 318 Kemeny, J.G. 51 310 322 Kim, K.H. 234 322 Kingman's Inequality 123 Kingman, J.R.C. 124 322 Kirchhoff's theorem 209 Kirkland, S. 234 320 322 Kleitman, D.J. 236 318 Knopp, P. 88 327 Koenig — Egervary theorem 70 Koenig's Theorem 70 Koenig, D. 59 62 63 69—72 322 Kohlberg, E. 260 322
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