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Bapat R.B., Raghavan T.E., Rota G.C. (Ed) — Nonnegative Matrices and Applications
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Название: Nonnegative Matrices and ApplicationsАвторы: Bapat R.B., Raghavan T.E., Rota G.C. (Ed)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: 352Добавлена в каталог: 12.05.2008Операции: Положить на полку |
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Предметный указатель
Konig — Egervary theorem 70 Konig, D. 59 62 63 69 70 71 72 322 Konig’s theorem 70 Koyak, R. 153 322 Krein, M.G. 54 322 Kronecker Index Theorem 84 118 158 247 Kronecker product 58 145 159 Kubo, F. 158 315 Kuczynski, M. 310 322 Kuhn — Tucker theorem 273 Kuhn, H.W. 102 108 109 322 Kullback, S. 272 320 Kwong, M.K. 144 316 Lagrange’s Theorem 21 Lai, A.K. 193 218 316 322 Lancaster, K. 275 282 291 322 Landis, T.L. 263 324 Laplace expansion 62 Latin rectangle 111 Least element 30 Left Perron eigenvector 21 Leontief input-output model 242 Leontief matrix 32 Leontief model of production 279 Leontief, W. 32 275 279 281 322 Levinger, B.W. 124 322 Levinger’s Inequality 122 123 Lewin, M. 67 322 Lewin’s Theorem 67 Lexicographic center 98 Lieb, E.H 236 321 Line of a matrix 69 Linear programming problem 22 Linear slave economies 279 Linear statistical model 156 Lipschitz continuous function 15 Littlewood, J.E. 80 149 204 321 Liu, J. 58 323 Local univalence theorem 302 Locally univalent 292 Loewy, R. 72 112 321 Log-concave sequence 184 Logarithmic convexity 159 London, D. 93 323 Loop 220 Lopes, L. 157 323 Lorentz 51 Lorentz transformation 52 Lorenz, J. 250 260 320 Lovasz, L 4 75 197 323 Lowner ordering 134 M -matrix 24 215 Majorization 149 Marcus, M. 62 93 157 323 Marek, I. 124 323 Markham, T.L 121 320 Markov chain 45 Markov, A.A. 46 51 Marshall, A. 153 273 323 Martos, B. 172 179 193 323 Marxian system 285 Maschler, M 102 323 Mason, J.H. 196 209 323 Mason’s conjecture 209 Matrix game 7 76 Matrix over the max algebra 219 Matrix-tree theorem 209 Matroid 196 Max algebra 219 Maximum likelihood principle 265 McKenzie, L.W. 311 323 Meek, R.L. 310 322 Mehta, M.L. 219 323 Mendelsohn, N.S. 64 321 Menon, M.V. 246 272 323 Merely positive subdefinite 167 Merris, R. 148 323 Metzler, L.A. 311 312 323 Meyburg, A. 245 327 Meyer, C.D. 51 323 Micchelli, C.A. 173 179 323 Miller, R.E. 275 323 Mine, H. 62 66 88 323 324 Minimax theorem 9 Minoux, M. 225 320 Minus partial order 156 Mirsky, L. 62 199 324 Mitra, S.K. 156 272 324 325 Mixed discriminant 200 Mixed volume 209 Mohan, S.R. 311 324 Moore — Penrose inverse 229 Morgenstern, O. 310 322 Morishima, M. 156 312 314 324 Morley, T.D. 156 158 160 315 324 Moser, W.O.J. 218 Mulmuley, K. 78 324 Multinomial distribution 186 195 265 Multiparameter 186 Multivariate 187 Murota, K. 72 324 Murty, U.S.R. 4 105 197 317 N-matrix 298 N-matrix of the first category 298 N-matrix of the second category 298 Negative hypergeometric distribution 195 Neumann, M. 134 319 320 Newman, M. 93 323 Nijenhuis, A. 236 324 Nikaido, H. 290 305 306 311 312 320 324 Nonnegative matrix 1 Nonsingular M-matrix 216 Nucleolus of the game 99 Null space 10 O1ech, C 311 324 Odell, P.L. 156 324 Ohlin, B. 311 324 Olesky, D.D. 290 316 Olkin, I. 153 273 323 Olsder, G.J. 225 315 318 324 Open shop scheduling 105 Operators leaving a cone invariant 54 Oppenheim, A. 137 143 144 153 324 Oppenheim’s inequality 137 143 144 153 Optimal assignment problem 72 73 Optimal intensity vector 288 Optimal price vector 288 289 Optimal solution 22 Optimal strategy 8 76 Ortega, J.M. 84 324 Oscillation ratio of Hopf 255 Ost, R. 124 134 322 Ostrowski, A.M. 24 28 260 324 Over max algebra 219 220 238 P-matrix 294 p-norm distance 177 P61ya, G. 80 149 182 204 206 321 325 Panov, A.A. 203 324 Parallel sum 153 Parlett, B.N. 246 263 Parter, S.V. 246 324 Parthasarathy, K.R. 165 325 Parthasarathy, T. 9 103 311 324 325 Partly decomposable matrix 66 Partly infinite vector 220 Pasinetti, L.L. 276 310 325 Path 4 38 56 65 68 210 213 218 220 Path-positivity 218 Pati, S. 234 316 Pattern 67 225 301 Peleg, B. 102 323 Perfectly stable market 306 Perkins, P. 41 325 Permanent 61 62 68 88 89 93 148 185 190 200 202 236 Permanent minimizer 89 Permanent-on-top conjecture 148 Permanental dominance conjecture 148 Permutation game 103 Permutation matrix 1 Perron eigenvalue 21 284 Perron eigenvector 21 284—286 Perron matrix 44 Perron root 21 286 Perron — Frobenius theorem 17 24 44 54 115 216 219 236 251 260 278 285 Perron, O. 1 4 5 15 16 17 23 24 34 38 43 44 47 54 57 115 116 120 121 122 123 132 133 134 159 178 179 184 196 210 211 212 216 219 225 236 237 251 259 260 275 278 284 285 309 310 325 Perron’s theorem 5 Phelps, R.R. 176 325 Plemmons, R.J. 25 235 317 325 Plummer, M.D. 75 323 Pointed 51 Pointed cone 251 Pole 24 Pollers, J.A.M. 103 105 319 Polyhedron 31 Polynomially positive matrix 44 Positive definite function 190 Positive definite matrix 25 134 197 201 204 216 Positive diagonal 61 Positive matrix 1 Positive semidefinite matrix 58 134 162 171 174 197 200 Positive subdefinite matrix 167 Power positive matrix 44 Power series 24 Prasada Rao, P.S.S.N.V. 234 325 Pratt, J.W. 260 322 Preemptive schedule 105 Pressman, S. 310 325 Primary good 277 279 283 Primitive matrix 40 Probabilistic algorithm 78 Probability density function 185 Productive economy 280 Pseudo-convex function 166 Ptak, V. 28 311 320 Pullman, N.J. 234 320 322 Pure exchange economy 276 Puri, M.L. 156 324 Putnam, C.R. 24 325 Pyke, R. 88 273 321 q -permanent 190 Quadrat, J.-R 225 318 Quandt, R. 246 325 Quasi-concave function 165 Quasi-convex function 165 Quasi-positive definite matrix 193 Quesnay, R 310 322 Radius of convergence 24 Rado’s Theorem 198 Raghavan, T.E.S. 9 28 44 83 100 102 150 246 250 311 316 317 325 327 Rajendra Prasad, V. 103 105 319 Random walk 45 Rank additivity 156 Rank function of a matroid 198 Rank k truncation 209 Rao, C.R. 156 274 325 Ratcliff, D. 267 319 Rathore, R.K.S. 194 325 Ravindran, G. 311 325 Real estate game 96 Recski, A. 199 325 Recurrent 47 Reduced 198 Reducible matrix 2 Regular splitting 25 Reid, J.K. 246 319 Reijnierse, H. 102 325 Reinsch, C. 246 324 Rheinboldt, W.C. 84 324 Ricardean system 285 Right Perron eigenvector 21 Rinott, Y. 189 322 Romanovskii, V.I. 51 325 Rook polynomial 236 Roos, C. 225 324 Ross, S. 265 325 Rota, G.C. 21 325 Rothaus, O.S. 88 325 Rothblum, U.G. 130 250 319 326 Roush, R W. 235 322 Rutman, M.A. 54 322 Ryser, H. 72 318 Sachs, H. 219 319 Saddle point 55 56 Sahi, S. 159 326 Sahni, S. 105 320 Saigal, R. 311 322 Samborskii, S.N 225 319 Samuelson, P.A. 276 290 308 310 311 312 321 326 327 Satisfaction 98 Scaling theorem 87 247 Scarf, H.E. 103 326 Schmeidler, D. 99 326 Schmidt, K. 165 325 Schneider, H. 57 72 130 246 250 319 326 Schneider, R. 209 326 Schrijver, A. 88 112 326 Schur complement 138 Schur power 145 190 Schur product 141 174 193 Schur, I. 115 123 137 138 139 141 142 145 146 148 151 153 154 155 174 187 190 193 326 Schur-concave function 187 Schur’s Inequality 137 Schur’smajorization theorem 137 151 Schwartz, J.T. 113 326 Schwarz, B. 159 326 Seidel, J.J. 218 219 326 Semiring 237 Seneta, E. 44 326 Separating hyperplane theorem 150 Series-parallel Inequality 156 Shapley, L.S. 95 102 103 323 326 Sheity, C.M. 64 273 Shorted operators 156 Shubik, M. 103 323 326 Sign change group 218 Signature matrix 299 Simple graph 198 Simple root 5 Singular value 238 Sinkhorn, R. 88 327 Skeel, R.D. 246 327 Skew-symmetric matrix 55 Slave economy 279 280 Slutsky equation 306 Slutsky, E. 306 327 Snell, J.L. 51 322 Solymosi, T. 100 102 327 Soules, G.W. 148 260 327 Soules’ conjecture 148 Spanning tree 208 Spectra of graphs 219 Speicher, R. 190 318 Sraffa System 282 Sraffa, P. 282 327 Sridhar, R. 311 324 Stability 305 Stable matrix 314 Stanciu, S. 193 327 Standard system 286 Stanford, D. 225 317
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