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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
$D_{1}AD_{2}$ Theorem      118
$P_{0}$- matrix      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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