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Minc H. — Nonnegative Matrices
Minc H. — Nonnegative Matrices



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Название: Nonnegative Matrices

Автор: Minc H.

Аннотация:

This text/reference is the most up-to-date volume on nonnegative matrices in print and presents much material that was previously available only in research papers. It is the only book to cover the van der Waerden conjecture on permanents. There is also coverage of doubly stochastic matrices and inverse problems. The material has abundant connections to graph theory, incidence geometry, stochastic processes, functional analysis, and quadratic forms. Each chapter contains a comprehensive set of problems and a substantial list of references.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 206

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
(0,1)-matrix      xi 68
(0,1)-matrix, doubly stochastic      118
Adjacency matrix      77
Adjoint matrix      xi
Adjugate (matrix)      xii
Aharoni, R.      73 103
Alexandrov, A.D.      129 130 139
Arc of a directed graph      76
Berge, C.      87 103
Berman, A.      159 165 193 195
Bipartite graph      101
Birkhoff, G.      117 118 119 139
Boullion, T.      165
Brauer, A.      31 33 46
Bregman, L.M.      97 103
Brualdi, R.      103
Caratheodory's theorem      119
Circuit      77
Circuit, Hamiltonian      77
Cogredient matrices      5
Collatz — Wielandt function      8
Collatz, L.      7 8 23
Column stochastic matrix      136
Compound (matrix)      xii
Compound (matrix), permanental      xiii
Conjugate (matrix)      xi
Convex, hull      167
Convex, polygon      167
Convex, sum      167
CYCLE      77
Cyclic matrix      47
Cyclic polygon      175 176
Dance Problem      72
de Bruijn, N.G.      90 103
Decomposable matrix      5
Decomposable matrix, nearly      87
Decomposable matrix, partly      82
Directed graph      76
Directed graph, minimally connected      87
Directed graph, strongly connected      77
Directed graph, vertex of      76
Discrepancy      112
Dmitriev, N.      172 174 175 176 193
Dominated matrix      36
Dominating nonnegative matrix      36
Doubly quasi-stochastic matrix      105
Doubly stochastic (0,1)-matrix      118
Doubly stochastic matrix      85 105
Doubly stochastic pattern      85
Dulmage, A.L.      103
Dynkin, E.      172 174 175 176 193
Edgar, G.      84 103
Edge of a graph      100
Egervary, E.      74
Egorycev, G.P.      128 129 130 136 137 139
Eigenvalue, maximal      11
Eigenvector, maximal      11
Elementary doubly stochastic matrix      106
Erdoes, P.      90 103
Exponent of an oscillatory matrix      154
Falikman, D.I.      128 129 140
Farahat, H.K.      119 140
Fiedler, M.      165 193
Fisher's Inequality      151
Frechet, M.      146 165
Friedland, S.      193
Frobenius form of an irreducible matrix      51 54
Frobenius — Koenig theorem      71 93
Frobenius, G.      1 8 11 19 23 24 26 33 46 47 49 51 53 54 56 67 71 75 80 103 121
Fully indecomposable matrix      82 99
Function, Collatz — Wielandt      8
Gantmacher (Gantmakher), F.R.      165 195
Generalized permutation matrix      xiii
Generalized Vandermonde matrix      163
Gersgorin, S.A.      146 165
Gibson, P.M.      96 103
Graph      101
Graph, bipartite      101
Graph, directed      76
Graph, directed, minimally connected      87
Graph, edge of      100
Hadamard product      xi 81
Hadamard's inequality      151
Hadamard's inequality for totally nonnegative matrices      154
Hall, M., Jr.      93 96 103 104
Hamiltonian circuit      77
Harary, F.      23 103
Hardy, G.H.      110 115 140 195
Hartfiel, D.J.      88 103
Hershkowits, D.      193
Hopcroft, J.E.      103
Imprimitive matrix      47
Incidence matrix      68
Incidence matrix of a bipartite graph      102
Indecomposable matrix      5
Indecomposable matrix, fully      82 99
Index of imprimitivity of a directed graph      79
Index of imprimitivity of an irreducible matrix      47
Induced matrix      xiii
Inverse eigenvalue problem      166
Inverse elementary divisor problem      166
Inverse spectrum problem      166
Irreducible matrix      5
Irreducible matrix, Frobenius form of      51 54
Irreducible matrix, index of imprimitivity of      47
Irreducible matrix, superdiagonal form of      54
k-indecomposable      99
Karp, R.M.      103
Karpelevic, F.I.      176 177 193
Kingman, J.F.C.      168
Knopp, P.      88 104
Knuth, D.      140
Koenig, D.      71 73 74 103 105 118 140
Krein, M.G.      165 195
Kronecker delta      xiii
Laplace expansion theorem for permanents      70
Ledermann, W.      28 29 33 41 46
Length of path      77
Lewin, M.      103
Line of a matrix      xi
Littlewood, J.E.      110 115 140 195
Loewy, R.      179 180 181 193
London, D.      134 136 140 179 180 181 193
Loop      77
M-matrix      159
Majorized nonnegative h-tuple      110
Mann, H.B.      93 103
Marcus, M.      19 23 39 46 49 67 83 103 109 119 120 121 122 123 124 126 131 132 135 140 165 193 195
Markov chain      141
Marshall, A.W.      140
Matching, perfect      100
Matrices, cogredient      5
Matrices, p-equivalent      82
Matrices, permutation equivalent      82
Matrix, (0,1)-      xi 68
Matrix, adjacency      77
Matrix, adjugate      xii
Matrix, column stochastic      136 141
Matrix, compound      xii
Matrix, compound, permanental      xiii
Matrix, cyclic      47
Matrix, decomposable      5
Matrix, decomposable, narly      87
Matrix, decomposable, partly      82
Matrix, dominated      36
Matrix, dominating nonnegative      36
Matrix, doubly quasi-stochastic      105
Matrix, doubly stochastic      85 105
Matrix, doubly stochastic, elementary      106
Matrix, fully indecomposable      82 99
Matrix, generalized permutation      xiii
Matrix, generalized Vandermonde      163
Matrix, imprimitive      47
Matrix, incidence      68
Matrix, incidence, of bipartite graph      102
Matrix, indecomposable      5
Matrix, indecomposable, fully      82
Matrix, induced      xiii
Matrix, irreducible      5
Matrix, k-indecomposable      99
Matrix, nearly decomposable      87
Matrix, nearly reducible      87
Matrix, nonnegative      xiii
Matrix, orthostochastic      106
Matrix, oscillatory      154
Matrix, p-equivalent      82
Matrix, partly decomposable      82
Matrix, positive      xiii
Matrix, primitive      47
Matrix, reducible      5
Matrix, row stochastic      141
Matrix, Schur-stochastic      106
Matrix, sign-regular      150
Matrix, sign-regular, strictly      151
Matrix, square root of      124
Matrix, Stjeltjes      165
Matrix, stochastic      141
Matrix, stochastic, column      141
Matrix, stochastic, doubly      85 105
Matrix, stochastic, row      141
Matrix, strictly sign regular      151
Matrix, superdiagonal block form of      54
Matrix, term rank of      74
Matrix, totally nonnegative      147
Matrix, totally positive      147
Matrix, transition      141
Matrix, tridiagonal      147
Matrix, unitary-stochastic      106
Maximal eigenvalue      11
Maximal eigenvector      11
Mendelsohn, N.S.      103
Minc, H.      3 19 23 39 41 46 49 55 57 58 60 61 62 63 64 65 67 83 90 93 96 97 103 104 109 120 121 122 123 124 134 140 165 187 189 193 195
Minimally connected directed graph      87
Minimizing doubly stochastic matrix      131
Mirsky, L.      63 67 119 140 193
Moyls, B.      39 109 120 121 122 123 140
Muirhead, R.F.      110 140
Nearly decomposable matrix      87
Nearly reducible matrix      87
Newman, M.      119 131 132 135 140
Nonnegative, matrix      xiii
Nonnegative, matrix, term rank of      74
Nonnegative, n-tuple      xiii
Normal form of reducible matrix      142
Olkin, I.      140
Orthostochastic matrix      106
Oscillatory matrix      154
Ostrowski, A.      29 30 33 41 46 165
p-equivalent matrices      82
Parter, S.      103
Partly decomposable matrix      82
Path      77
Path, length of      77
Pattern, doubly stochastic      85
Pattern, zero      xiii
Perfect matching      100
Perfect, H.      183 184 194
Permanent      xii 69
Permanental compound      xiii
Permutation equivalent matrices      82
Perron, O.      8 11 23 47
Plemmons, R.J.      159 165 193 195
Polygon, cyclic      175 176
Poole, G.      165
Positive matrix      xiii
Positive n-tuple      xiii
Primitive matrix      47
Product, Hadamard      xi
Ptak, V.      165
Pullman, N.J.      67
Reducible matrix      5
Reducible matrix, normal form of      142
Ree, R.      126 140
Roberts, E.J.      104
Rosette      87
Row stochastic matrix      141
Ryser, H.J.      93 103
Salzmann, F.L.      194
Schneider, H.      103
Schrijver, A.      97 98 104
Schur, I.      80 105 106 107 140
Schur-stochastic matrix      106
SDR      68
shrink      87
Sign-regular matrix      150
Sign-regular matrix, strictly      151
Sinkhorn, R.      88 104
Spanning subgraph      76
Square root of a matrix      124
Stjeltjes matrix      165
Stochastic matrix      141
Stochastic matrix, column      141
Stochastic matrix, doubly      85 105
Stochastic matrix, row      141
Strictly sign-regular matrix      151
Strongly connected directed graph      77
Subgraph      76
Subgraph, spanning      76
Suleimanova, H.R.      183 194
Superdiagonal ($n_{1}$, $n_{2}$, ..., $n_{k}$)-block form      54
Superdiagonal block form      54
Swift, J.      194
Sylvester's identity      152
Sylvester, J.J.      54 67 152
System of distinct representatives      68
Term rank      74
Totally nonnegative matrix      147
Totally positive matrix      147
Transition matrix      141
Tridiagonal matrix      147
Unitary-stochastic matrix      106
Van der Waerden conjecture      128
Van der Waerden, B.L.      128 140
Vandermonde matrix, generalized      163
Varga, R.S.      104
Vertex of a convex polygon      167
Vertex of a directed graph      76
Wielandt, H.      7 8 23 36 46 47 51 67
Zero pattern      xiii
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