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| Hilton H. — Homogeneous linear substitutions |
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| Предметный указатель |
Absolute invariant 40
Adjoint bilinear form 77
Adjoint Hermitian form 78
Adjoint quadratic form 78
Alternate substitution 34
Alternate substitution with given invariant-factors 184
Bertrand's theorem 110
Bilinear form 63
Canonical form of real orthogonal substitution 47
Canonical shape of family of bilinear forms 173
Canonical shape of family of Hermitian forms 177 180
Canonical shape of family of quadratic forms 175
Canonical shape of Hermitian form 66 74
Canonical shape of real quadratic form 67 74
Canonical substitution 29 59
Cayleyan orthogonal substitution 171
Characteristic-determinant 20
Characteristic-equation 20
Characteristic-equation of direct product 27
Characteristic-root 20 66
Characteristic-root of alternate substitution 43
Characteristic-root of Hermitian or real symmetric substitution 42
Characteristic-root of unitary substitution 37 46
Characteristic-root, common to two substitutions 25
Co variant of quantic 41
Coefficients of substitution 9
Collineation 90
Commutative substitutions 10
Congruent transformation 63
Conicoids 98 104
Conies 103
Conjugate substitution 17
Constituent of direct product 26
Contragredient transformation 72
Critical values of real quadratic form 96
Cyclant substitution 12
Definite Hermitian form 67
Definite Hermitian form, Hermitian substitution 34
Definite real quadratic form 68
Degree of substitution 9
Determinant of substitution 9
Direct product 26
E( unit substitution) 10
Einheit 10
Elementartheiler 52
Family of alternate forms 180
Family of bilinear, Hermitian, or quadratic forms 172
Generalized coordinates 107
Geometrical movements 94
Hamilton — Cayley relation 82
Hermitian form 65
Hermitian form, invariants 155
Hermitian form, substitution 34
Homogeneous linear substitution 9
Homographic transformation 90
Invariant 38
Invariant of quantic 41
Invariant-factors of alternate substitution 134
Invariant-factors of canonical substitution 56
Invariant-factors of determinant 52
Invariant-factors of direct product 55
Invariant-factors of inverse substitution 57
Invariant-factors of product of alternate substitution and real multiplication 55
Invariant-factors of product of alternate substitution and symmetric substitution 138
Invariant-factors of product of Hermitian substitution and real multiplication 55 144
Invariant-factors of product of two alternate substitutions 136
Invariant-factors of product of two Hermitian substitutions 142
Invariant-factors of substitution 54
Inverse of canonical substitution 28
Inverse substitution 13
Involution pencil 177
Lagrange's differential equation 86
Linear differential equations 83
| Linear differential equations, homogeneous equations 88
Linear differential equations, invariant 147
Linear differential equations, invariant-factor 58
Linear differential equations, substitution 9
Linearly dependent substitutions 78
Matrix of substitution 9
Maxima and Minima of real quadratic form 96
Minkowsky's Theorem 16
Monomial substitution 26
Movement (geometrical) 94
Multiplication 26
Negative Hermitian form 67
Negative Hermitian form, real quadratic form 68
Normal substitution 22
Order of a direct product 27
Order of a substitution 14
Orthogonal substitution 84 38
Oscillations about a position of equilibrium 107
Permutable substitutions 10
Permutation 26
Pole 19
Poles of direct product 27
Positive Hermitian form 67
Positive Hermitian form, real quadratic form 68
Powers of a canonical substitution 28
Powers of a substitution 13
Principal coordinate 84 108
Product (direct) 26
Product (direct) of alternate and symmetric substitution 137
Product (direct) of alternate substitutions 135
Product (direct) of Hermitian substitution and a real multiplication 144
Product (direct) of Hermitian substitutions 120 142
Product (direct) of symmetric substitutions 122
Product (direct) of two or more bilinear forms 63
Product (direct) of two or more substitutions 10 11
Projective transformation 90
Quadratic form 64
Quadratic form, invariant 146
Quartic equation 95
Quasi-Hermitian substitution 144
Quasi-Hermitian substitution, with given invariant-factors 145
Rank of determinant 50
Rank of Hermitian form 66
Real substitution 34
Reducing cubic 95
Relations between powers of a substitution 79
Relative invariant 40
Schaar 172
Self-corresponding points 91
Similarity substitution 26
Simple invariant-factor 58
Skew-symmetric determinant 34
Standard type of alternate bilinear form 75
Standard type of bilinear form 68
Standard type of symmetric bilinear form 73
Substitution 9
Substitution with Hermitian invariant 169
Substitution, permutable with given substitution 112
Substitution, permutable with substitutions permutable with given substitution 117
Substitution, transformable into its inverse 61 169
Substitution, transformable into orthogonal substitution 160
Substitution, whose q-th power is given 116
Sum of substitutions 78
Tangential equations 103
Thomson's theorem 110
Transform of a substitution 17
Transformation of one alternate substitution into another 140
Transformation of one orthogonal substitution into another 161
Transformation of one symmetric substitution into another 128
Transposed substitution 17
Unit substitution 10
Unitary substitution 34 39
Variables of a substitution 9
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