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Bapat R.B., Raghavan T.E.S. — Nonnegative Matrices and Applications
Bapat R.B., Raghavan T.E.S. — Nonnegative Matrices and Applications



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Название: Nonnegative Matrices and Applications

Авторы: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 336

Добавлена в каталог: 07.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Kojima, M.      311 322
Kolmogorov, A.N.      46 51 322
Kolmogorov-Chapman equations      46
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
Lal, 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's Inequality      122 123
Levinger, B.W.      124 322
Lewin's Theorem      67
Lewin, M.      67 322
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
Loewner ordering      134
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
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's conjecture      209
Mason, J.H.      196 209 323
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
Minc, 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, R      290 305 306 311 312 320 324
Nonnegative matrix      1
Nonsingular M-matrix      216
Nucleolus of the game      99
Null space      10
Odell, P.L.      156 324
Ohlin, B.      311 324
Olech, C.      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's inequality      137 143 144 153
Oppenheim, A.      137 143 144 153 324
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, F.      124 134 322
Ostrowski, A.M.      24 28 260 324
Over max algebra      219 220 238
P-matrix      294
p-norm distance      177
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's theorem      5
Perron, O.      1 4 5 15—17 23 24 34 38 43 44 47 54 57 115 116 120—123 132—134 159 178 179 184 196 210—212 216 219 225 236 237 251 259 260 275 278 284 285 309 310 325
Phelps, R.R.      176 325
Plemmons, R.J.      25 235 317 325
Plummer, M.D.      75 323
Pointed      51
Pointed cone      251
Pole      24
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
Potters, J.A.M.      103 105 319
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.-P.      225 318
Quandt, R.      246 325
Quasi-concave function      165
Quasi-convex function      165
Quasi-positive definite matrix      193
Quesnay, F.      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, F.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—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's inequality      137
Schur's majorization theorem      137 151
Schur, I.      115 123 137—139 141 142 145 146 148 151 153—155 174 187 190 193 326
Schur-concave function      187
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
Shetty, 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' conjecture      148
Soules, G.W.      148 260 327
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
Stanley, R.P.      209 327
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