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| Turnbull H.W. — An Introduction to the Theory of Canonical Matrices |
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| Предметный указатель |
Absolute invariant 37 154
Adjoint matrix 4 43 161 164
Adjugate determinant 4
Aitken, A. C. 81 142
Algebra, non-commutative 143 150
Alternant 59 60 63 81 158 161
Analytical dynamics 1 161 171 178
Apolarity, vector of 121
Associate matrices 32—33
Associative law 3 20
Augmented matrix 29—30
Autonne 181
Auxiliary unit matrix 62 143—1444 151—155
Axes, principal 1 170
Axisymmetric determinant 99
Axisymmetric determinant, matrix 11 15 32 101 106 164—165
Basis 46 135 142
Basis, change of 117
Bazin 179
Bellavitis 165
Bendixson 110 111
Bibliography of matrices, Muir 178
Bibliography of matrices, Rasch 166
Bicomplementary sets 80
Bilinear forms 15 19
Bilinear forms, differentiated 173
Bilinear forms, families of 30
Bilinear forms, invariant 38
Bilinear forms, pencil of 114 129—131
Bilinear forms, reciprocal 162
Bilinear forms, singular pencil of 129—130
Bilinear forms, symmetric 83
Binary p-ic matrix 21
Binary p-ic matrix, quantic 56
Binary p-ic matrix, vectors 119
Binet 31 73
Binet — Cauchy theorem 9 25 28
Bordered determinant 161
Born 178
Brauer 110 111
Brioschi 98 111
Bromwich 110 111 142
Brown, O. E. 142
Browne, E. T. 110 111 183 184
Burnside 56
Canonical reductions of matrices, collineatory, classical 58 60 75
Canonical reductions of matrices, collineatory, of Jacobi 64 80 81
Canonical reductions of matrices, collineatory, rational 45 49
Canonical reductions of matrices, collineatory, real 72
Canonical reductions of matrices, congruent, of Jacobi 94
Canonical reductions of matrices, congruent, rational 138—139
Canonical reductions of matrices, equivalent, of Smith 22—23
Canonical reductions of matrices, geometrical meaning of 53—54
Canonical reductions of matrices, uniqueness of classical 67
Canonical reductions of pencil of quadratics 115—116 132—135 141 142 182
Canonical reductions of pencils, classical 116
Canonical reductions of pencils, rational 116
Canonical reductions of pencils, real 72 182
Canonical reductions of singular pencils 125—135
Cauchy 9 25 26 31 73 111
Cayley 9 30 56 107 112 166 178
Cayley matrix operator 178
Cayley matrix operator, orthogonant 107
Cayley — Hamilton theorem 43—44 180
Chains of isolated elements 60 69
Chains of isolated elements, of vectors 49
Characteristic determinant 41
Characteristic determinant, equation 41
Characteristic determinant, function 41
Characteristic determinant, function of vector 43
Characteristic determinant, reduced, equation 48
Characteristic determinant, reduced, function 46—52 161—162
Characteristic determinant, Segre 61 64 70 79
Christoffel 111
Chrystal 178
Cipolla 99
Classical canonical form 58 60 75
Clebsch 111
Cogredient variables 37 38
Collineation 36
Collineation, as successive polar reciprocation 153 182
Collineation, geometrical meaning 40 42
Collineation, reciprocal 40
Collineation, singular 40 142
Collineatory sub-group 35 37
Collineatory sub-group, transformation 11 12 13
Combinants 113
Commutantat functions 148
Complete diagonal 65
Compound commutants 148
Compound commutants, determinants 28
Compound commutants, matrices 27 73 90 93 98 180
Compound commutants, quadratic forms 91
Conditioned maxima and minima 170
Confluent alternant 60 63 81
Confluent alternant, difference-product 60 63 75 81 150
Conformable matrices 3
Congruent See Canonical reductions
Congruent, group 36—37 82
Congruent, reduction of Hermitian form 84
Congruent, transformation 11 12 13
Conics 1 82
Conics, congruent reduction 82
Conics, pencils of 115 118 182
Conjugate matrices 32—33
Conjugate matrices, partitions 80
Conjunctive reduction of skew form 87
Conjunctive reduction of skew form, sub-group 36
Continued fractions 74 75 182
Contragredient variables 37
Convergence of matrix functions 73 81
Correlation 37
Correlation, canonical form of 84 138—139 140—141
Correlation, statistical 174—175 178
Courant 178
Cpmmutants 143 145 147—149
Criteria for denniteness 91
Criteria for denniteness, for rank 92—93
Darboux 142 164 165 166
Definiteness 89—90
Definiteness, criteria for 91
Delta, Kronecker 151
Dependence of vectors 45
Dependence of vectors, of vector pencils 119
Determinant 3 4 28 41
Determinant, alternant 51 60 63 75 81
Determinant, characteristic 41
Determinant, compound 28
Determinant, recurrent 56
Determinant, skew symmetric 99
Determinant, with matrix elements 76
Diagonal, complete 65
Diagonal, secondary 11
Diagonatthatrix 7—8
Diagonatthatrix, partitioning 7
Dickson 56 81 84 141 142
Difference equations 176—177
Difference with matrix factors 77—78
Difference-product 59
Difference-product, confluent 60 63 75 81
Differential equations 1 176—177
Differentiated bilinear form 173
Differentiated bilinear form, matrix 180
Dirac 151 166
Dual sets of integers 80
Dynamical equilibrium 161 171 178
Elementartheiler 30 69 108 180
Elementary divisors 69 108 180
Elementary divisors, matrix 48 56—57 62
Elementary divisors, of pencil 117 136 180
| Elementary divisors, transformations 10—13
Elements, isolated 8
Ellipse, semi-axes of 170 171
Ellipsoid 171
Equations, difference 176—177
Equations, differential 176—177
Equations, incompatible 29
Equations, linear algebraic 10 13 29
Equations, linear matrix 143 145 148 166
Equations, normal, of Least Squares 173
Equations, singular linear algebraic 29
Equilibrium, dynamical 161 171 178
Equivalent matrices 19
Equivalent matrices,  -matrices 26
Equivalent matrices, pencils 116—117
Equivalent matrices, singular pencils 129
Euclid 18 22
Factors, invariant 27 30
Factors, matrix and scalar 15
Factors, of pencils 116—117
Factors, of pencils of Hermitian forms 119
Factors, symmetric, of general matrix 152—153
Families of forms 30 See
Ferrers 80
Fibonacci numbers 75
Field 20 45
Fischer 99
Forms, bilinear and quadratic 15
Forms, families of 30
Forms, hermitian 34
Forms, invariant or latent 37—39
Forms, linear 45
Forms, pairs of 106—107
Forms, pencils of 114 130—131
Franklin 183
Function, generating, of key quadratics 158—159
Function, maxima and minima of real 168—169
Function, of matrix 7 73 81 149
Function, of normal frequency 174—175 See
Functional equation of resohent 161
Gauss 18 98
Generalized rotation 102
Geometrical meaning of collineation 40 42 53 54 153
Geometrical meaning of collineation, of congruent group 82 115 181 182
Geometry, co-ordinate 1 9 170—171
Grade of vector 47 53
Group 20
Group, properties 20 34—35
Group, sub-groups of equivalent 19 32—36
H.C.F. process 17
H.C.F. process for polynomials 16 21—22
Hadamard's Theorem 97 98
Hamilton 9 43 44
Hawkes 81
Heisenberg 178
Hensel 81
hermite 18 44 111
Hermite polynomials 102
Hermitian matrices and forms 32—34 44
Hermitian matrices and forms, congruent reduction of 84
Hermitian matrices and forms, invariant factors of 119
Hermitian matrices and forms, latent roots of 101 106
Hermitian matrices and forms, pencils 114 130—131 166
Hermitian matrices and forms, reduction of 133—134 141 142
Hermitian matrices and forms, singular case 134—135
Hermitian matrices and forms, skew 33—34 98
hessian 18
hilbert 161 178
Hilton 142 166
Hirsch 110 111
Hitchcock 166
Image points 40
Imaginary matrices 33 34
In variance of minimal indices 120—121
Ince 178
Incompatible equations 29
Indicatrix 167
Indices, minimal 120—121
Inequalities in principal minors of definite determinant 98 177
Inertia, law of 89
Infinite matrices 3 166
Ingraham, M. H. 142
Inner product 3 15 37 38
Interpolation formula of Lagrange 76
Interpolation formula of Lagrange, of Sylvester for matrices 76—77 81 160
Invariant bilinear forms 38 143
Invariant bilinear forms, quadratic forms 154
Invariant factors 27 30
Invariant factors, of pencil 116 117 119
Invariants 37 154
Invariants, of singular pencil 128
Inverse factorial series 74
Involutory matrices 33 103
Isolated elements and minors 8
Isolated elements and minors, semi-isolated 8
Isotropic vector 103
jacobi 44 64 80 81 94 98 99
Jacobi, collineatory canonical form of 64
Jacobi, congruent canonical form of 94
Jessop 166
Jordan, C. 80 181
Jordan, P. 178
Kantor, S. 142
Kelvin 99
kinetic energy 171
Kowalewski 56
kronecker 98 141 142
Kronecker, delta 151
Lagrange 98 170 172
Lagrange, -matrices 14 16 21 44 54 55 176
Lagrange, interpolation formula 76
Lagrange, undetermined multipliers 170
Landsberg 56 81
Latent forms 37 38 39 143 154
Latent forms, matrices 106 159
Latent forms, points 44
Latent forms, primes 154
Latent forms, quadratic forms 155
Latent roots, theorems on, definition and general 41 44
Latent roots, theorems on, inequalities in 110 111 183 184
Latent roots, theorems on, of Hermitian and real symmetric 101 106
Latent roots, theorems on, of Hermitian principal minors 101 172
Latent roots, theorems on, of induced and compound matrices 73 183
Latent roots, theorems on, of orthogonal and unitary 107 108
Latent roots, theorems on, of orthogonal principal minors 110 111
Latent roots, theorems on, of skew and skew Hermitian 101 106
Lattes 56
Law, associative 3 20
Law, commutative 3
Law, of inertia 89
Law, reversal 4
Least squares 9 173
Ledermann, W. 142
Legendre polynomials 102
Linear algebraic equations 10 13 29
Linear algebraic equations, dependence 45
Linear algebraic equations, difference equations 176—177
Linear algebraic equations, differential equations 176—177
Linear algebraic equations, forms 45
Linear algebraic equations, matrix equations 143 145 148 166
Linear algebraic equations, transformations 13
Loewy 110 111
Logsdon 141
MacDuffee, C. C. 179
Matrices, combinantal 113
Matrices, conformable 3
Matrices, pencils of 113
Matrices, permutable 116 180
Matrix, adjoint 4 161 164
Matrix, alternant 59 158 161
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