|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Gurevich G.B. — Foundations of the theory of algebraic invariants |
|
|
|
| Предметный указатель |
Absolute, plane in Euclidean geometry 81
Addition of doublets 32 94
Affine quantity 35
Affinor 338
Affinor, unit 339
Aggregate, Pfaff 387
Algebra, Lie Matrix 131
Alternation 110
Alternation, symbolic 225
Alternation, total 136
Angle between vectors in multi-dimensional Euclidean space 97
Annihilator 296
Area, orientated 128
Axis 122
Axis of reflection 17
Axis of transformation 21 397
Base of a linear manifold of forms 239
Base of a linear manifold of vectors 346
Base of a linear pencil of binary forms 253
Basis theorem of Hilbert 239
Bivector 105
Bivector, simple 118 381
Cayley curve 324
Centre of pencil of straight lines 58
Centre of transformation of principle group 21
Characteristics, algebraic 251
Characteristics, arithmetic 252 258
Characteristics, Weierstrass 350
Class of algebraic curve 320
Classification of pencils of binary quadratic forms 258
Classification of tensors of given order 245
Coefficient, leading, of the covariant of a binary form 304
Collineation of projective space 125
Combinant of a system of mixed forms 257
Commutator of two matrices 131
Complex, linear, of k-dimensional planes 366
Complex, linear, of straight lines 123
Complex, symbol 371
Components, affine, of a vector 24
Components, effective, of a tensor 103 105
Concomitant of a form 141
Concomitant of a tensor 140
Concomitant, joint, of several tensors 140
Concomitant, mixed, several tensors 142
Contraction of tensors 112 113
Contraction of tensors, total 113
Contravariant of a form 142
Contravariant tensor 106 107
Convention of Einstein 25
Coordinate points of a multidimensional affine space 90
Coordinate points of a multidimensional projective space 87
Coordinates, affine, of a geometric object 10 37 100
Coordinates, affine, of a point 23
Coordinates, affine, of a second order curve 33
Coordinates, affine, of a straight line 29
Coordinates, axial, Pluecker, of a straight line 122
Coordinates, Cartesian, of a second order curve 8
Coordinates, Cartesian, of a straight line 6
Coordinates, homogeneous, Cartesian, of a point in a plane 51
Coordinates, homogeneous, Cartesian, of a straight line 40
Coordinates, of a hyperplane 88 93
Coordinates, of a second order hypersurface 116
Coordinates, Pluecker, contravariant, of a k-dimensional plane 364
Coordinates, Pluecker, contravariant, of a straight line 122
Coordinates, Pluecker, covariant, of a k-dimensional plane 364
Coordinates, projective, of a point of a plane 52
Coordinates, projective, of a point of a plane, straight line 42
Coordinates, projective, second order curve 62
Coordinates, projective, straight line on a plane 54
Coordinates, radial, Pluecker, of a straight line 122
Correlation of projective space 123
Covariant of a form 142
Covariant tensor 101
Curve of second class 65
Curve, first polar, of a curve of order r 324
Degree of a covariant 142
Determinant of affine transformation 27 90
Determinant of linear transformation of space 99
Determinant of n contravariant vectors 145
Determinant of n covariant vectors 146
Determinant of projective transformation 43 53 86
Determinant, bordered 158
Direction, isotropic 397
Direction, orientated 129
Direction, orientated, plane 129
Direction, orientated, r-dimensional 416
Discriminant of binary cubic forms 154
Discriminant of binary forms of order r 320
Discriminant of binary quadratic forms 49 249
Discriminant of n-ary quadratic form 147
Discriminant of symmetric contravariant second order tensor 157
Discriminant of symmetric covariant second order tensor 147
Discriminant of ternary cubic form 325
Discriminant of ternary quadratic form 62
Divisibility of a polyvector by a vector 356
Divisibility of a polyvector by alternated product of vectors 356
Doublet 31 94
Doublet, coordinate 38
Equality of contravariant vectors in multidimensional affine space 92
Equality of doublets 31 94
Equality of tensors 108
Equation of Hamilton — Cayley 342
Equation, characteristic, of two ternary quadratic forms 316
Equation, tangential 65 150
Equivalence of figures 20 36
Equivalence of tensors 245
Expansion of an alternation with respect to an index 342
Factor, symbolic, of first kind 190
Factor, symbolic, of second kind 191 192
Factor, symbolic, of third kind 192
Finishing line of a doublet 31
Form, bilinear 116
Form, binary 141
Form, binary, quadratic 104 115
Form, characteristic, of pencil of quadratic forms 256
Form, cubic 104
Form, multilinear, of contravariant vectors 102
Form, multilinear, of covariant and contravariant vectors 107
Form, multilinear, of covariant vectors 106
Form, multilinear, of order r of n variables 104
Form, multilinear, symmetric 114
Form, n-ary 141
Form, of a set of variables 141
Form, of order r of contravariant vector 104
Form, of order r of covariant vector 104
Form, relative 134
Form, ternary 141
Form, ternary, quadratic 308
Form, trilinear 102
Formula of Laguerre 83
Formula of Newton 351
Formula of Waring 351
Geometry, affine 35 91
Geometry, affine, in complex domain 37 91
Geometry, affine, in real domain 37 91
Geometry, affine, multi-dimensional 91
Geometry, Euclidean, multi-dimensional 95
Geometry, Lobachevskian 83
Geometry, Minkowskian 83
Geometry, projective 65
Geometry, projective, in complex domain 88
Geometry, projective, in real domain 88
Geometry, projective, multi-dimensional 88
Geometry, projective, of the plane 51
Geometry, projective, of the straight line 40
Geometry, Riemannian 83
Group of linear transformations of space 99
Group of matrices of order n 131
Group of motions 14 98
Group of motions and reflections 17 96
| Group property 14
Group, affine 22 98
Group, principal 18
Group, projective 41 54 97
Group, unimodular, of linear transformations 113
Harmonic property 47 58
Hermite's reciprocal law 307
Hessian of a form 153
Hessian of an r-th order curve 321
Homology parabolic 414
Homology, non-parabolic 414
Hyperplanes of a finite doublet 144
Hyperplanes of a regular linear complex 368
Hyperplanes of multidimensional affine space 93
Hyperplanes of multidimensional projective space 88
Hyperplanes, conjugate with respect to a second order hypersurface 413
Hyperplanes, conjugate, with point, with respect to linear complex of straight lines 381
Hyperplanes, coordinate 89
Hyperplanes, diametral, of second order hypersurface 338
Hyperplanes, independent 88
Hyperplanes, parallel 93
Hyperplanes, polar, of points with respect to second order hypersurface 124 329
Hyperplanes, tangent to a second order hypersurface 150 329
Hypersurface 95
Hypersurface of class r 117
Hypersurface of order r 117
Hypersurface of, central 126
Hypersurface second class 117
Hypersurface second order 116
Hypersurface, algebraic 117
Identity, first fundamental 211
Identity, second fundamental 211
Identity, third fundamental 212
Invariant 1
Invariant, absolute 19 139
Invariant, algebraic 159
Invariant, arithmetic 146
Invariant, integral, rational 159
Invariant, integral, rational, homogeneous 164
Invariant, joint 8
Invariant, joint, of several tensors 140
Invariant, metric 17
Invariant, of a form 141
Invariant, of a tensor 139
Invariant, of group of motions 16
Invariant, relative 19 139
Involution 150
Involution, elliptic 252
Involution, hyperbolic 252
Involution, parabolic 253
Involutions, pencil of 260
Jacobian of a system of forms 152
Jordan canonical form of an affinor 349
Kronecker delta 53
Law of compliments 258 392
Law of inertia of quadratic forms 336
Length of a vector in multi-dimensional Euclidean space 96
Lie matrix algebra 131
Matrix algebra of Lie 131
Method, symbolic, of Aronhold 189
Minor, reduced 27
Motion 13 98
Multiplication of affinors 339
Multiplication of doublet by number 31 94
Multiplication of tensors 111
Multiplication of tensors with contraction 112
n-hedron, coordinate 87
n-hedron, polar, of second order hyperplane 413
n-vector 105
n-vector, unit, contravariant 135
n-vector, unit, covariant 135
Null-system 124
Number of dimensions of a linear set of vectors 346
Number of dimensions of a space 86 90
Object, geometric, affine 37 91
Object, geometric, Cartesian 10
Object, geometric, projective 65 87
Object, geometric, with respect to group of motions 16
Object, geometric, with respect to linear transformation of space 100
Operation  295
Operation O 296
Order of a covariant 142
Order of a general tensor 106 107
Order of a group of matrices 131
Order of a matrix algebra of Lie 131
Order of a space 85
Order of a tensor 101 106
Origin of affine coordinates 24 92
Pairs of hyperplanes dividing each other 90
Pairs of hyperplanes of a pencil not dividing each other 90
Pairs of points of a straight line dividing each other 46 89
Pairs of points of a straight line dividing each other harmonically 47
Pairs of points of a straight line not dividing each other 46 89
Pairs of straight lines not dividing each other 58
Pairs of straight lines of a pencil dividing each other 58
Pairs of straight lines of a pencil dividing each other harmonically 58
Parabola, isotropic 397
Parallelogram, coordinate 38
Pencil of binary quadratic forms 253
Pencil of hyperplanes 89
Pencil of straight lines 58
Pencils, projective, of straight lines 315
Pfaff aggregate 387
Plane, k-dimensional of multidimensional affine space 94
Plane, k-dimensional of multidimensional projective space 89
Plane, k-dimensional, of affine space 94
Plane, k-dimensional, tangential to second order hypersurface 329
Plane, projective 51
Planes, k-dimensional, conjugate with respect to second order hypersurface 374
Planes, k-dimensional, parallel 95
Planes, multidimensional, conjugate with respect to linear complex of straight lines 381
Point at infinity of straight line 40
Point external with respect to second order curve 315
Point internal with respect to second order curve 315
Point of inflection of curve of order r 321
Point of multidimensional affine space 89
Point of multidimensional projective space 86
Point of multiplicity p of curve of order r 323
Point of view of group theory 20
Point, circular, at infinity 81
Point, conjugate with respect to linear complex of straight lines 381
Point, conjugate with respect to second order curve 63
Point, conjugate with respect to second order hypersurface 116
Point, coordinate 43 61 87
Point, diagonal, of perfect quadrangle 66
Point, double, of curve of order r 318
Point, double, of projective transformation of straight line 50
Point, fixed, of transformation 16
Point, independent 57 89
Point, regular, of plane 51
Point, regular, of straight line 41
Point, singular, of curve of order r 318
Point, singular, of linear complex 367
Point, singular, of second ordersurface 148
Polar Invariant 230
Polar line of points with respect to second order curve 64
Polarity 124
Pole of hyperplane with respect to second order hypersurface 337
Pole of straight line with respect to second order curve 64
Polynomial, characteristic, of an affinor 342
Polyvector 105
Polyvector, simple 354
Polyvectors, correlative 366
Power of an affinor 339
Power of points with respect to a circle 396
Power, oblique, of an affinor 341
Principle of Clebsch 319
Principle of duality 60 89 106
Process, invariant 223
Process, polar 230
|
|
|
| Реклама |
|
|
|
|
|
|
|
|
О проекте