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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Minc H. - Nonnegative Matrices |
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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 ( ,  , ...,  )-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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