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Gurevich G.B. — Foundations of the theory of algebraic invariants
Gurevich G.B. — Foundations of the theory of algebraic invariants

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Название: Foundations of the theory of algebraic invariants

Автор: Gurevich G.B.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 435

Добавлена в каталог: 17.12.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\Omega$      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
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