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Schneider H. (ed.) — Recent advances in matrix theory
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Название: Recent advances in matrix theory
Автор: Schneider H. (ed.)
Аннотация: The theory of matrices goes back to Sylvester and Cayley, particularly to Cayley's famous memoir of 1858. The subject Is thus classical and central In the mathematical tradition. This century, mathematical progress has been richer and more rapid than ever before.
New mathematical disciplines have arisen, several of which have their roots In matrix theory. This is true of the structure theory of algebras. Functional analysis generalizes many familiar results on matrices. Recently there has been vigorous development in the use of matrices In combinatorial problems. In turn these fields have
strongly Influenced more recent developments in matrix theory. The matrix theorist must not confine his interests to only one branch of modern mathematics. Rather, he must be a technician whose special skills are applied to problems in algebra, analysis, computation, number theory, combinatorial analysis or topology as the need arises. Conversely, workers in these fields may find a knowledge of recent progress in matrices useful. To these, as well as the matrix specialists, the present volume is addressed.
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Рубрика: Математика /
Серия: Сделано в холле
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 1964
Количество страниц: 142
Добавлена в каталог: 17.03.2011
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Предметный указатель
133
Absolute 49
Afriat 137
Albert 137
Alpha-width 107
Aronszajne 136
arrow 133
Bartels 132
Bauer, F.L. 130
Bellman 132 136 137
Birkhoff 86
Bordering 136
Brauer, A. 127 130 132 138
Brenner 136 137 138
Browne 130
Bueckner's theorem 45
Carlson 133
Characteristic polynomials of product of matrices 138
Characteristic roots, simplicity of 83
Class 122
Class 110
Class 104
Column sum vector 104
Comparability 98
Comparability, constant 94
Comparable 94
Completely non negative 137
Compound matrix 136
Condition number 130
Convex body 46
Convex body, cone 87
Convexity 134
Cournat 136
Cross-ratio 87 91
David 122
Davis, C. 126 135
Decomposable 62
Diagonals 137
Dominant 137
Dominant root 127
Double interchange 113
Downing 132
Drazin 134
Dungey 134
Elementary divisors 84
Elements, rearrangements of 138
Elements, replacing of 136
Equilibrated 46
Exclusion region 39
Exclusion region theorem 39 53
Exponent, of even 4
Factor analysis 137
Fan 129 130 135 136 137
Farahat 138
Feingold 55 137
Fiedler 55 125 126 136 137
Fisher, M.E. 132
Flanders 134
Ford 122
Forsythe 125 130 132 137
Foster 131
Frebenius 134
Friedman 136
Fulkerson 115 121 122 123
Fuller, A.F. 132
Functional analysis 81
Functionals 94
Functionals, linear positive 94
Functionals, r-multilinear 61
Gale 123
Gantmacher 123 137
Gauss Seidel iteration method 132
Gauss transformation 137
Generalized stochastic matrix 10
Gershgorin 39 57 128
Gershgorin circle sets 129
Gershgorin theorem 53
Gerstenhaber 134 135
givens 136
Goddard 138
Goldstine 130
Golub 130
Gross 121
Gruenberg 134
Haber 108 123
Hadamard inequality 137
Hadamard tournament matrix 122
Hadamard — Schur product 136
Haynsworth 137
Hermitian matrices, products of 133
hilbert 87
Hilbert matrix 137
Hoffman, A.J. 115 122 126 130 136 137
Hopf, E. 92
Horn 130 132 136 137
Householder 128 133 136 137
Incidence matrix 103 132
Inclusion region 39
Inclusion region, theorem 39 42 47
Indecomposable 127
Initial part of row 115
Interchange 106
Interchange, theorem 106
Invariant 103 106
Inverse-characteristic value problem 132
Irreducible class 121
Irreducible class, components 120
Irreducible class, matrix 119
Johnson 123
Kac 134
Kantorovich 57
Kato 127
Kingman 135
Koenig 107 123
Kotelyanskii 127 128 136 137
Krein 137
Kronecker, product of 136
Krylov iterates 43
Landau 110 123
Lax, A. 127 135
Least square problem 130
Lebesque — Stieltjes integral 92
Lederman 138
Lehmann 41
Lewis, D.C. 136
Liapunov, theorem of 133
Lidskii 132 135
Lie algebras 134
Liederman 136
Line of matrix 106
Localization theorem 39
Loewy 132
lotkin 137
Lowner 135
Majorization 104 127
Marcus 121 123 132 135 136 137
Matrices 127
Matrices with identical characteristic equations 138
Matrices, commuting 134
Matrices, moment 44
Matrix function 64
Matrix, block diagonal 136
Matrix, commuting 136
Matrix, double stodhastic 66
Maximal comparable part 98
Maximal matrix 104
McAndrew 115 122
McCoy 134
Miller 135
Minc 123 135
Minimax theorems 41
Minkowski inequality 137
Moez, Amir 130 132
Monotone column sum vector 104
Monotone row sum vector 104
Monotone tournament matrix 110
Monotonic 49
Monotonicity 134
Moon 123
Moser 121 124
Motzkin 134 137
Nirschl 39 41 55 137
Non negative matrices 127
Norm 46
Normalized class 107
Normalized class, matrix 109
Nudel’man 132
Number theoretical problem 131
Oldenburger, R., lemma of 81
Operator, completely symmetric 63
Operator, permutation 63
Operator, skew symmetric 63
Operator, symmetry 63
Oppenheim 137
Ore 123
Osborne, E.E. 138
Ostrowski 55 126 128 130 132 133 136 137 138
Pall 137
Parker, W.V. 130 138
Permanent 64
Perron's theorems 81
Perturbation 125
Polar decomposition 135
Positive matrices 81
Positive matrices, operators 92
Power-positive 4
Power-positive of odd exponent 4
Projective metric 86
Property L 127 134
Property P 134
Ptak 55
Rayleigh quotient theorem 39 42
Reduced 4
Reducible matrix 119
Relaxation method 137
Rellich 126
Robertson 138
Rothe, W.E. 138
Round robin matrix 109
Round robin tournament 109
Row sum vector 104
Ryser 123
Schneider, H. 39 41 133 134
Schroeder 57
schur 83
Schwarz, B. 138
Separation locus 43
Separation locus, polynomial 43
Separation locus, theorems 42
Shoda 132
Singular values 130
Size of matrix 103
Skew symmetric 63
Stable 132
Stable, stable D 133
Stable, stable H 133
Stable, stable S 133
Stein, P. 134
Steinberg, R. 136
Stochastic 128
Strang 136
Straus 130 132
Subdeterminants 136
Svarcman 132
Swanson 49
Symmetric product 63
Symmetrization 129
Symmetry class 63
Taussky 127 130 132 133 134 136 138
Tensor product 62
Tensors 4
Tensors, contravariant 62
Term rank 106
Terminal part of row 115
Thompson, R.C. 136 132
Todd, J. 130 133
Tournament matrix 109
Transition point 118
Triangle inequality 98
Uniformly positive 99
Unreduced 4
Van der Waerden, conjecture of 66
Varga 55 128 133 136 137
Vector lattices 87
Vector, oscillation of a 97
Vector-lattice 97
von Neumann 130
Weinberger 135
Weyl, H. 130 135
Wiegmann 135
Wielandt 49 126 132 133 135 136
Williamson 137
Young D., successive overrelaxation 132
Zassenhaus 133
Zero-one matrix 103
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