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Seneta E. — Non-negative matrices: an introduction to theory and application
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Название: Non-negative matrices: an introduction to theory and applicationАвтор: Seneta E. Аннотация: Since its inception by Perron and Frobenius, the theory of non-negative matrices has developed enormously and is now being used and extended in applied fields of study as diverse as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming, while its development is still proceeding rapidly as a branch of pure mathematics in its own right. While there are books which cover this or that aspect of the theory, it is nevertheless not uncommon for workers in one or other branch of its development to be unaware of what is known in other branches, even though there is often formal overlap. One of the purposes of this book, through its aiming at breadth rather than depth, is to relate various aspects of the theory, insofar as this is possible.
Язык: Рубрика: Математика /Серия: Сделано в холле Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1974Количество страниц: 256Добавлена в каталог: 23.05.2011Операции: Положить на полку |
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Metzler, L.A. 34 40 Metzler’s Theorem 34 Miller, H.D. 83 Minc, H. 55 56 57 Minkowski matrix 40 Minkowski, H. 40 Minors, all 34 171—181 Minors, leading principal 28 34 35 41 49 171—181 Mirsky, L. 56 ML matrix 40 48—49 Morgenstern, O. 34 Morishima matrix 48 Morishima, M. 32n 33 48 Mortality-fertility conditions 76 Mott, J.L. 117 118 121 Moy, S.-T.C. 156 177 178 Mustafin, H.A. 117 118 119 120 Nelson, E. 156 Neveu, J. 156 Norm, Euclidean 80—82 191—192 Number theory 40 182—185 Numerical analysis 27 Oldenburger, R. 38n 80n 92n Operators on sequence spaces 156 178 Operators, finite-dim.extensions of Perron — Frobenius theory 48 Operators, linear, mapping convex cone 48 Optimal choice condition 60 Optimal productivity 66 Optimization 59—60 66 Orey, S. 156 Ostenc, E. 118 Ostrowski, A.M. 47 55 Paithasarathy, K.R. 151 Parlett, B.N. 83 Patter, S.V. 48 57 Patterns, of stochastic matrices 106 Patterns, recurrence of 107 Paz, A. 23 118 119 120 121 205 Perfect, H. 56 Perkins, P. 54 Permanent, of a matrix 57 Perron matrix 43—49 Perron — Frobenius eigenvalue 20 Perron — Frobenius eigenvalue, algebraic multiplicity of 8 Perron — Frobenius eigenvalue, bounds for 6 23 28 55 Perron — Frobenius eigenvalue, geometric multiplicity of 8 Perron — Frobenius eigenvectors 20 59—67 168 172 179 Perron — Frobenius theorem 1 7 25 46—47 Perron — Frobenius theory 7 20 Perron — Frobenius theory for infinite P 125 156 177—178 Perron — Frobenius theory, extensions of 40 43 48 Perron — Frobenius theory, other approaches 23 Perron — Frobenius theory, Wielandt’s approach 22—23 Perron, O. 22 Philips, R.S. 184n Poincare, H. 99 Poisson — Martin representation 142 147—152 Pollard, H. 156 Polya urn scheme 89 118 Polynomial, modified characteristic of T 180 Potentials, non-decreasing sequence of 146 Potentials, theory of 142—147 156 178 Power-positive matrix 43—48 Probability, first passage 141 Probability, hypergeometric distribution of 101 Probability, initial distribution of 86 91 97—99 Probability, measures 150—152 Probability, stationary distribution of 86 91 97 Probability, transition 85—86 Probability, ‘taboo’ 125 141 Pruitt, W.E. 177 Ptak, W. 23 47 54 Putnam, C.R. 178 Quine, M.P. 78n Quirk, J. 48 R-classification of irreducible P 168—171 R-classification of irreducible T 161 Radius, common convergence 26 61 161—181 Random walk (matrix) 88 95—97 101 158—159 179 Recurrence time, mean 127 Recurrence, criterion for 128 Recurrent event (matrix) 88—89 152—155 169 176—177 181 Regularity of M.C. 97 99—102 Regularity, positive 99—100 Resolvent 187 Rheinboldt, W.C. 205 Riesz decomposition 147 Robert, F. 205 Romanovsky, V.I. 23 99 100 Rosenberg, R.L. 39 Rosenblatt, D. 23 54 Samelson, H. 23 Samuelson, P.A. 48 Sarymsakov — Mustafin Theorem 118 Sarymsakov, T.A. 100 117 118 118n 119 120 178 179 Schneider, H. 24 48 55 57 118 Schutzenberger, H.P. 119 Schwartz, S 54 Scrambling property 108 109 117—120 Sedlacek, J. 23 Seneta, E. 47 66 67 118 158n 178 179 180 Sidak, Z. 55 156 178 Simon, H.A. 33 Sinkhorn, R. 57 Sirazhdinov, S.H. 121 Snell, L.J. 34 77 97n 99 155 156 Solidarity properties 134 165 171 178 Solow, R. 34 48 Space, unitary 191 Spectrum, localization of 55—57 Spitzer, F. 77 State space, non-constant 89 118 Stein — Rosenberg theorem 38—39 Stein, P. 39 Stochasticity assumption, asymmetry of 160 Strategy, homogeneous 66 Styan, G.P.H. 205 Subinvariance Theorem 20 60 134 Sucheston, L. 205 Suleimanova, H.R. 56 Superconvexity, in non-negative matrices 82—83 Tambs — Lyche matrix 40 Tambs-Lyche, R. 40 tappo-Danilevskii, J.A. 22 Taussky.O. 49 Theorem, Bolzano — Weierstrass 150 Theorem, Central Limit for M.C.’s 100 119 Theorem, Coale — Lopez 77 Theorem, Erdoes — Feller — Pollard 156 Theorem, Ergodic for regular M.C.’s 97 Theorem, Ergodic, for primitive M.C.’s 91 138 Theorem, General Ergodic, for primitive P 138 Theorem, Helly’s 151 Theorem, Markov’s 117 Theorem, Metzler’s 34 Theorem, Perron — Frobenius 1 7 25 46—47 Theorem, Riesz Decomposition 147 Theorem, Sarymsakov — Mustafin 118 Theorem, Schur’s 80 190—191 Theorem, Stein — Rosenberg 38—39 Theorem, Strong Ergodicity, for T 73 Theorem, Subinvariance 20 60 134 Theorem, Weak Ergodicity, for T 69 Thomasian, A.J. 119 Timan, O.Z. 56 Titchmarsh, E.C. 16 In Transformation, T to P 163—164 Transformation, unitary 190—192 Transience, criterion for 128 Transience, geometric 169 Transience, strong 177 180 Transient M.C.’s 140 147 Truncations of infinite T 171—181 Truncations of positive recurrent P 177—181 Truncations, of infinite P 176—181 Tweedie, R.L. 178 Types of incidence matrices 107 Ullman, J.L. 26 Urban 99 Van der Waerden, B.L. 57 Vandergraft, J.S. 205 Varga, R.S. 22 23 25 38n 39 47 54 56 Vector, decomposition of superregular 145 Vector, demand 31 35 Vector, external input 33 Vector, integral representation of superregular 147—152 Vector, invariant 140—142 Vector, minimal superregular 143 Vector, potential of column 144 Vector, regular 142—152 Vector, subinvariant 140—142 Vector, subinvariant row 134 Vector, superregular 142—152 Vector, superregular row 157 Vector, supply 31N Veech, W. 156 Vere-Jones theory of infinite T 177—181 Vere-Jones, D. 57 156 177 178 von Mises, R. 99 100 Weierstrass property 150 Wielandt, H. 22 23 24 25 47 48 54 Wielandt’s proof 22—23 Wolfowitz, J. 117 119 Wong, Y.K. 34 35 Woodbury, article of 34 Words, in stochastic matrices 119—121
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