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| Gurevich G.B. — Foundations of the theory of algebraic invariants |
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| Предметный указатель |
Product of a contravariant vector and a number in multidimensional affine space 92
Product of a doublet by a number 31 94
Product of affinors 339
Product of an isation affinor and a number 339
Product of tensors 112
Product, alternated, of vectors 112
Product, scalar, of a covariant and a contravariant vector 30 144
Product, scalar, of two vectors in multidimensional Euclidean space 96
Projections of points from  on to  369
Projective quantity 65
Property, affine, of figures 35
Property, group 14
Property, projective, of figures 65
Propositions, correlative 60
Propositions, dual 60
Quadrangle, perfect 66
Quadri-vector 105
Quantity, affine 35
Quantity, projective 65
r-vector 105
Radius vector 24 92
Range of points 56
Rank of a bivector 156
Rank of a covariant r-vector 157 353
Rank of a linear complex of straight lines 385
Rank of a non-symmetric second order tensor 157
Rank of a pencil of quadratic forms 256
Rank of a quadratic form 148
Rank of a symmetric covariant tensor 156
Rank of a symmetric second order covariant tensor 148
Rank of a system of linear equations 176
Rank of a system of points 66
Rank of a system of vectors 146
Rank of a tensor with respect to one of its indices 157
Rank of a trivector 156
Rank of an affinor 157
Ratio of two bivectors 127
Ratio, cross-, of four hyperplanes of a pencil 90
Ratio, cross-, of four points of a straight line 45 89
Ratio, cross-, of four straight lines of a pencil 58
Ray 122
Reflection with respect to a straight line 17
Renormalisation of coordinates 57
Resolvent, cubic 289
Resolvent, quadratic 264
Resultant of two binary quadratic forms 221 256
Root, characteristic, of an affinor 343
scalar 108
Scalar, absolute 134
Scalar, relative 133
Segment in multidimensional affine space 95
Semi-invariant of binary form 303
Series of Jordan — Clebsch 278
Set of four points, equianharmonic 48
Set of four points, harmonic 47 50
Shear 127 374
Signature of a quadratic form 334 335
Space, affine 90
Space, of a polyvector 353 354
Space, projective 86
Square, scalar, of a vector in multidimensional Euclidean space 96
Starting line of a doublet 31
Straight line of multidimensional affine space 95
Straight line of multidimensional projective space 89
Straight line, external with respect to second order curve 315
Straight line, improper of plane 52
Straight line, isotropic 81
Straight line, projective 40
Straight line, secant of second order curve 315
Straight lines, conjugate with respect to second order lines 68
Straight lines, coordinate 61
Straight lines, dependent, in plane 58
Straight lines, independent, of space of n-dimensions 385
Sum of affinors 339
Sum of contravariant vectors in multidimensional space 92
Sum of doublets 32 94
Sum of tensors 111
Surface, k-dimensional 95
Symbol, ordinary 371
| Symbol, parallel 193
Symbolic of Aronhold 189
Symmetrization of a tensor 108
System, complete of invariants 235
Systems of affine coordinates 90
Systems of projective coordinates 86
Syzygy 248
Syzygy of Cayley 268
T-system of curves 77
Tangent to a line of order r 318
Tangent to a line of order r at its double point 318
Tangent to a second order curve 63
Tensor, absolute 134
Tensor, contravariant 106
Tensor, covariant 101
Tensor, equal to zero 108
Tensor, equivalent 245
Tensor, metric 78 96
Tensor, mixed 107
Tensor, relative 134
Tensor, skew symmetric 105
Tensor, skew symmetric, with respect to several indices 105
Tensor, skew symmetric, with respect to two indices 105
Tensor, structural, of Lie algebra 133
Tensor, symmetric 103
Tensor, symmetric with respect to several indices 103
Tensor, symmetric with respect to two indices 103
Tensor, with constant components 170
Tensors, equal 108
Term of a transvectant 273
Terms, adjacent, of a transvectant 273
Theorem of Boole 231
Theorem of Cayley 390
Theorem of Ceva 84
Theorem of Desargues 67 138
Theorem of Hilbert 239
Theorem of Menelaus 84
Theorem of Pascal 315
Theorem of Steiner 315
Theorem, basis, of Hilbert 239
Theorem, first fundamental, of the symbolic method 206
Theorem, fundamental, of invariant theory 188
Theorem, second fundamental, of the symbolic method 213
Three pairs of points of involution 50
Trace of an affinor 340
Transformation linear of space 99
Transformation, affine 21 90
Transformation, homothetic 18
Transformation, projective 43 54 87
Transformation, projective, elliptic 50
Transformation, projective, hyperbolic 50
Transformation, projective, involutionary 50 352
Transformation, projective, parabolic 50
Transformations, linear, contragredient 59 100
Translation, parallel 31
Transvectant of order k 225 226
Transvectant, index of 225 226
Triangle, coordinate 61
Triangle, of points of inflection of third order curve 412
Triangle, polar, of second order curve 68 311
Trivector 105
Type of a tensor 245
Types, complimentary 258 263 392 393 395
Vector belonging to the space of a polyvector 354
Vector function, linear, of the first kind 130
Vector of invariable direction of an affinor 343
Vector of null direction of an affinor 341
Vector, conjugate with respect to a second order hypersurface 338
Vector, contravariant 26 91 99
Vector, coordinate 24 92
Vector, covariant 29 94 100
Vector, imaginary 189
Vector, imaginary, parallel 193
Vector, real 189
Weight of a relative tensor 134
Weight of a scalar 134
Weight of a term of an integral rational invariant 165 168
Weight of an invariant 139
Weight of component of a relative tensor 168
Weight of component of an absolute tensor 165
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