Marcus M., Minc H. — Survey of matrix theory and matrix inequalities :: Электронная библиотека попечительского совета мехмата МГУ

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Marcus M., Minc H. — Survey of matrix theory and matrix inequalities

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Название: Survey of matrix theory and matrix inequalities

Авторы: Marcus M., Minc H.

Аннотация:

Concise yet comprehensive survey covers broad range of topics: convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, much more.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 180

Добавлена в каталог: 06.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

-vector      2
-square matrix      2
th adjugate      16
(, , $\lambda$ )-matrix      13 129
(, , $\lambda$ )-matrix, adjoint of      25
(, , $\lambda$ )-matrix, determinant of      25
(, , $\lambda$ )-matrix, determinantal divisors of      42 46
(, , $\lambda$ )-matrix, normality of      72
Adjoint, (adjugate)      13
Adjoint, (conjugate transpose)      5
Adjoint, reduced      125
Adjugate      13
Aitken, A. C.      89 90
Alternant matrix      15
Alternating multilinear function      13
Amir-Mo $\acute{e}$ z, A. R.      89
Arithmetic-geometric mean inequality      106
Aronszajn, N.      134
Arscott, F.      171
Augmented matrix      31
Basis      29
Basis, completion to      38
Beckenbach, E. F.      134 135
Bellman, R.      89 171
Bendixon’s theorems      140
Bendixson, I.      140 171
Bergstrom, H.      134
Bilinear functional      59
Bilinear functional, conjugate      59
Binet — Cauchy theorem      14
Binet — Cauchy theorem for permanents      20
Birkhoff, U.      07 136
Block multiplication      6
Block multiplication, examples      7
Bodewig, E.      89
Bonnesen      135
Brauer, A.      145 148 155 156 170 171
Brauer’s Theorem      145 155
Bromwich, T. J. I’a.      171
Browne, E.      89 143 144 148 171
Browne’s theorem      143 144
Bullen, P.      136
Cauchy inequalities      119
Cauchy — Schwarz inequality      61
Cayley parameterization      74
Cayley — Hamilton theorem      50
Characteristic matrix      21
Characteristic polynomial      21
Characteristic roots      22
Characteristic roots, algebraic multiplicity of      39
Characteristic roots, geometric multiplicity of      38
Characteristic vectors      39
Circulant      66
Circular matrix      75
Collar, A. R.      89
Collatz, L.      136 171
Column of a matrix      2
Column vector      2
Companion matrix      52
Compound matrix      16
Concave      102
Concave, strictly      102
Congruence      81
Conjugate transpose      5
Conjunctive matrices      84
Convex combination      96
Convex function      101
Convex hull      96
Convex matrix function      112
Convex polyhedron      96
Convex sets      93
Convex sum      96
Convex, strictly      102
Coordinate      2
CYCLE      11
Cycle, disjoint      11
Cycle, length of      11
Cycle, structure      11
De Bruijn, N. G.      9
Decomposable      122
Decomposable, partly      123
Derogatory      50
Desplanques, J.      140 146 171
Determinant      12
Determinant, expansion by row or column      13
Determinant, Laplace expansion of      14
Determinantal divisors      41
Diagonal      12
Diagonal, main      12
Diliberto, S. P.      9
DIMENSION      29
Direct product      8
Direct sum of matrices      5
Direct sum of vectors      7
Discrepancy of two vectors      111
Distinct representatives      18
Dmitriev, N. A.      171
Doubly stochastic      95 129
Drazin, M. A.      9
Duncan, W. J.      89
Dungey, J. W.      91
Dynkin, E. B.      171
Eaves, J. C.      90
Eggleston, H. G.      135
Eigenvalues      23
Elementary divisor      43
Elementary matrix      33 37
Elementary operations      32
Elementary operations, column      37
Elementary operations, row      32
Elementary symmetric function      10
Elementary symmetric function, weighted      106
Entry      2
Epstein      91
Equivalent matrices      42
Euclidean norm      18
Euclidean space      60
Faddeeva, V. N.      89
Fan, K.      134 136 152 171 172
Fan’s theorem      152
Farnell, A. B.      144 148 172
Farnell’s inequality      144
Fass, A. L.      89
Fenchel, W.      135
Ferrar, W. L.      89
Field of values      168
Finkbeiner, D.      89
Fischer, E.      134
Flanders, H.      91
Fr $\acute{e}$ chet      159 172
Fr $\acute{e}$ chet’s theorem      159
Frazer, R. A.      89
Friedman, B.      91
Frobenius canonical form      53
Frobenius inequality      27
Frobenius theorem on commutativity      25
Frobenius theorem on nonnegative matrices      152
Frobenius, G.      136 144 172
Fuller, L. E.      89
Fully indecomposable      123
Functions of a matrix, arbitrary      73
Functions of a matrix, exponential      72
Functions of a matrix, normal      71
Functions of a matrix, polynomial      73
Functions of a matrix, square root      71
Gantmacher, F. R.      89 135 171
Gelfand, I.      89
Ger $\hat{s}$ gorin discs      146
Ger $\hat{s}$ gorin, S. A.      140 145 146 172
Ger $\hat{s}$ gorin’s theorem      146

Givens, W.      91 172
Gr $\ddot{o}$ bner, W.      89
Graeub, W.      89
Gram — Schmidt process      60
Grassmann product      17
Greatest common divisor      40
Grimshaw, M. E.      89 135
Gruenberg, K. W.      91
H $\ddot{o}$ lder inequality      108
Hadamard determinant theorem      114
Hadamard product      120
Hadamard, J.      140 146 171
Hadley, G.      89
Half-spaces, closed      94
Half-spaces, open      94
Halmos, P. R.      89
Hamburger, H. L.      89 135
Hamiltonian matrix      75
Hardy, G. H.      136
Heinz, E.      134
Hermite normal form      34
Hermite normal form, reduction to      35
Hermite normal form, use in solving equations      35
Hermitely congruent matrices      84
Hermitian      62 164
Hermitian form      69
Hirsch, A.      140 172
Hirsch, K. A.      89
Hirsch’s theorems      140 141
Hodge, W. V. D.      89
Hoffman, A. J.      91 134 172
Hoffman, K.      90
Hohn, F. E.      90
Homogeneous function      103
Hua, L. K.      91 136
Hypercompanion matrix      52
Hyperplane      94
Identity matrix      2
Incidence matrix      18
INDEX      83 84
Index of imprimitivity      124 128
Index sets      9
Induced matrix      20
Inner product      60
Invariant factors      43
Inverse of a matrix      3
Irreducibility      56
Ising model      26
Jacobi matrices      166
Jacobson, N.      90
Jaeger, A.      90
Jordan normal form      54
Jung, H. W. E.      90
K $\ddot{o}$ nig, D.      136
Kantorovich Inequality      110 117
Kantorovich, L. V.      136
Kato      91
Khan, N. A.      136
Kotelyanski $\breve{\imath}$ , D.      152 172
Kowalewski, G.      90
Kronecker delta      2
Kronecker product      8
Kronecker product, matrix product in terms of      9
Kuiper, N. H.      90
Kunze, R.      90
L $\acute{e}$ vy — Desplanques theorem      145 146
L $\acute{e}$ vy, L.      140 145 172
Lagrange identity      110
Laplace expansion theorem      14
Laplace expansion theorem, for permanents      20
Latent roots      23
Ledermann, W.      153 154 155 172
Ledermann’s theorem      153
Length of a vector      60
Lexicographic order      10
Lidski $\breve{\imath}$ , V. C.      172
Line      94
Line segment      93
linear combination      28
Linear dependence      29
Linear equations      30
Linear equations, equivalent systems      33
Linear equations, homogeneous      31
Linear equations, inconsistent systems      35
Linear equations, nonhomogeneous      31
Linear equations, trivial solution to      31
Linear functional      101
Linear independence      29
Littlewood, J. E.      136
Lopes, L.      136
Lyapunov, A.      160 171
Lyapunov’s theorem      160
MacDuffee, C. C.      90 171
Marcus      91 135 136 137 172
Matrix      1
Maxfield, J. E.      137
Maximal root      124
McGregor, J. L.      136
Metzler, W. H.      90
Mine, H.      137 172
Minkowski determinant theorem      115
Minkowski inequality      109
Minkowski, H.      146 172
Mirsky, L.      90 136 137 172
Monic polynomial      40
Motzkin, T. S.      91
Moyls, B. N.      137 172
Muir      90
Multiplication of matrices      2
Multiplication of matrices, and vectors      3
Multiplication of matrices, by blocks      6
Multiplication of matrices, in terms of rows and columns      4
Murdoch, D. C.      90
Negative, definite      69
Negative, semidefinite      69
Neiss, F.      90
Nering, E. D.      90
Newman      91 135 137 149
Newton’s inequalities      106
Nilpotent matrix      5
Nilpotent matrix, example of      4
Nonderogatory      50
Nonnegative -tuple      121
Nonnegative (positive semidefinite)      69
Nonnegative matrix      121 152
Nonnegative orthant      95
Nonsingular matrix      3
Norm      40
Norm, Euclidean      18
Norm, of a vector      60
normal      62 161
Normal, real      63
Null space      31
Nullity      31
Orthogonal      63
Orthogonal, complex      63
Orthonormal      60
Orthostochastic      95
Ostrowski, A.      145 154 155 156 160 170 172 173
Ostrowski’s theorems      150 151 154
Ovals of Cassini      149
P $\acute{o}$ lya, G.      136 137
Paige, L. J.      90
Pairwise orthogonal      60
Parker, W. V.      90 144 148 173
Parker’s inequality      144
Parodi      171
Partitioned matrices      6
Pedoe, D.      89
Pencil of matrices      79

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