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| Авторизация |
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| Поиск по указателям |
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| Hodge W.V.D., Pedoe D. — Methods of Algebraic Geometry: Volume 1 |
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| Предметный указатель |
Integral domain, indeterminate over 21
Integral domain, quotient field of 15
Intermediary line in projectivity 218
Intersection in an incidence space 211
Intersection in Grassmann coordinates 304
Intersection of linear spaces 189
Invariant factors of  -matrix 92
Invariant of null-polarity 380
Invariant of polarity 372
Inverse matrix 55 81
Inverse of element in a group 4
Involution on a line 352
Involutory homology 356
Involutory homology, particular collineation 355
Involutory homology, transformation 352
Irreducible polynomial 27
Isobaric 155
Isomorphism between rings 10
Isomorphism, skew 175
Jacobi's theorem on determinant of submatrix of adjugate matrix 82
Jacobian 133
Jacobian matrix 133
Join of fundamental spaces in a collineation 336
Join of linear spaces 189
Join of linear spaces in an incidence space 211
Join of linear spaces in Grassmann coordinates 306
Kronecker delta 54
Laplace's expansion of determinant 75
Latent roots of a matrix 95
Law of composition 2
Leading term of polynomial 142
Left-hand projective space or  185
Left-hand vector 48
Left-hand vector, row of matrix as 56
Line, meeting vertices of fundamental stars 342
Line, united, containing only one united point 350
Linear complex 381
Linear dependence 43
Linear dependence of one point on others in projective space 182
Linear dependence of points in an incidence space 208 268
Linear dependence, in  180
Linear homogeneous equations 68
Linear homogeneous equations, manifold of solutions 69
Linear homogeneous equations, right-hand 69
Linear homogeneous equations, solution by determinants 84
Linear independence 43
Linear non-homogeneous equations 85
Linear set 41
Linear set, basis for 45
Linear set, dimension of 45
Linear set, left-hand 41
Linear set, minimal basis for 45
Linear set, right-hand 42
Linear space 183 208
Linear space with given Grassmann coordinates 312
Linear space, basis for 183
Linear space, equations of 188
Linear space, generic 315
Linear spaces, intersection of 189 211
Linear spaces, join of 189 211
Lying in, relation between linear spaces 184
Manifold of solutions of linear homogeneous equations 69
Matrices 49
Matrices over a commutative field 71
Matrices, postmultiplication of 51
Matrices, premultiplication of 51
Matrices, product of 51
Matrices, ring of square 7 54
Matrices, square 54
Matrices, sum of 50
Matrix product 51
Matrix rank 65
Matrix, adjugate 81
Matrix, characteristic 95
Matrix, characteristic function of 95
Matrix, column printed as row 50
Matrix, complement of 72
Matrix, compound 291
Matrix, determinant of 74
Matrix, determinant of product 78
Matrix, division into blocks 53
Matrix, Jacobian 133
Matrix, regular 55
Matrix, ring 54
Matrix, rows as vectors 60
Matrix, singular 72
Matrix, skew-symmetric 86
Matrix, square root of 96
Matrix, submatrix 52
Matrix, symmetric 86
Matrix, transformations of 58
Matrix, transpose of 66
Matrix, transpose of product 72
Matrix, zero 51
Minimal algebraic basis 108
Minimal basis of linear set 45
Minimum function of matrix 96
Minus sign, multiplicative property 10
Multiplication of matrices, associative law 52
Multiplication of matrices, distributive law 52
Multiplication of points on a line 256
Negative of element in additive group 4
Non-commutative field 39
Non-commutative group 3
Non-Desarguesian geometry 213
Non-homogeneous equations 162
Non-homogeneous linear equations 85
Non-singular correlations 426
Non-singular projective transformations 322
Non-special collineation 336
Null-polarity 366 378
Null-polarity, canonical form for 380
Null-polarity, invariant of 380
Odd permutation 5
One-to-one correspondence 10
One-to-one correspondence, defined by perspectivity 216
Order of square matrix 362
Pappus' theorem 203
Pappus' theorem, consequences of 274
Partial derivatives 121
Particular collineations 354
Particular collineations with only one fundamental space 356
Particular involutory collineation 355
Pencil of lines 216
Permissible transformations for reduction of correlation 399
Permutation, even, odd 5
Perspective ranges 216
Perspective, triangles in 192
Point in projective space 178
Point triad 245
Point, algebraic 179
Point, rational 179
Point, symbolic notation for 181
Point, transcendental 179
polarities 367
Polarity 366
Polarity, canonical form 368 372
Polarity, conjugate points in 367
Polarity, conjugate spaces in 375
Polarity, invariant of 372
Polarity, vertex of 374
Polynomial 20
Polynomial rings 19
Polynomial, characteristic, of algebraic element 102
Polynomial, coefficients of 20
Polynomial, completely reducible 112
Polynomial, degree of 20
Polynomial, derivative of 119
Polynomial, divisor of 25
Polynomial, irreducible 27
| Polynomial, leading term of 142
Polynomial, primitive 33
Polynomial, root field of 114
Polynomial, root of 114
Polynomial, symmetric functions of roots of 115
Polynomial, total degree of 115
Polynomial, zero of 114
Polynomials, in a non-commutative ring 23
Polynomials, relatively prime 20
Polynomials, specialisation of 22
Polynomials, Taylor's theorem for 122
Postmultiplication of matrices 51
Premultiplication of matrices 51
Prime ideal 168
Prime ideal, element of integral domain 28
Prime or  211
Primes, equivalent, in integral domain 30
Primes, star of, in projective space 339
Primitive element of algebraic extension 126
Primitive element of polynomial 33
Principle of duality 190
Product of matrices 51
Product of projective transformations 177
Projective correspondence between points and spaces 326
Projective number space 176
Projective number space, extension of 178
Projective ranges 217
Projective space of n dimensions 178
Projective space, point in 178
Projective transformation 322
Projective transformation, canonical form 323
Projective transformation, dual 323
Projective transformation, exceptional points of 322
Projective transformation, non-singular 322
Projective transformation, rank of 323
Projective transformation, singular 322
Projective transformation, singular space of 325
Projective transformation, vertex of 325
Projective transformations 177 322
Projective transformations, group of 177
Projectively identical invariant constructions 231 238
Projectively identical linear spaces 186
Projectivities, fundamental, on a line 278
Projectivity or chain of perspectivities 217
Projectivity, equation of, on a line 281
Proper divisor of a polynomial 25
Properties of infinity 280
Propositions of incidence 185 208
Quadrangle 244
Quadrangular set of points 245
Quadratic p-relations for Grassmann coordinates 309
Quadratic p-relations, alternative form 312
Quadric 375
Quadric, envelope incidence 427
Quadric, incidence, of correlation 427
Quaternions 40
Quotient field of integral domain 15
r-way spaces 206
Range of points 216
Ranges in perspective 216
Ranges, homographically related 217
Ranges, projectively related 217
Rank of a matrix 65
Rank of a matrix, column-rank 66
Rank of a matrix, connection with determinants in commutative case 84
Rank of a matrix, row-rank 60
Rank of projective transformation 323
Rational point of projective space 179
Reference system in incidence space 249
Regular element, or unit, of ring 13
Regular matrix 55
Related coordinate systems 283
Related ranges 216
Relation of one linear space lying in another 184
Relatively prime polynomials 26
Remainder theorem 25
Representation of incidence space as a 259
Restricted type of allowable transformation 367
Restrictions on the geometry in an incidence space 272
Resultant ideal 166
Resultant ideal for set of binary equations 156
Resultant ideal of (n+1) homogeneous equations in (n+1) unknowns 170
Resultant ideal of two binary forms 150
Resultant ideal, system for equations in several unknowns 159
Resultant, properties of 152
Resultant-forms 166
Right-hand linear homogeneous equations 69
Right-hand vectors 48 65
Right-hand vectors, columns of matrix as 66
Ring 6
Ring of coefficients of set of equations 146
Ring of square matrices 54
Ring without characteristic 14
Ring, characteristic of 14
Ring, condition for field 13
Ring, condition for integral domain 13
Ring, not a u.f.d. 29
Ring, polynomial 19
Ring, regular element, or unit, of 13
Ring, unit, or regular element of 13
Ring, unity of 12
Rings 6
Rings, classification of 12
Rings, equivalence between 10
Rings, extension of 11
Rings, isomorphic 10
Rings, subrings 11
Root field of a polynomial 114
Root of polynomial 114
Roots, latent, of a matrix 95
Row-rank of a matrix 60
Rows of matrix as vectors 66
Rule for determining fundamental space of collineation 336
Rule for determining vertex of united primes of dual collineation 339
Scale coordinate systems 283
Scale on a line 253
Segre symbol for collineations 350
Segre symbol for singular collineations 361
Self-conjugate points  in a null-polarity 382
Self-conjugate points in a polarity 367
Set of coordinates of point in projective space 178
Set, linear 41
Signed minor or cofactor 77
Similar collineations 328
Simple algebraic extensions 99
Simple correlations 390
Simple correlations, geometrical properties 419
Simplex in an incidence space 211
Simplex of reference in projective space 182
Singular collineations 358
Singular collineations in [3] 361
Singular collineations in [3], Segre symbol 361
Singular collineations, Segre symbol 361
Singular correlations 422
Singular correlations of first and second kind 423
Singular matrix 72
Singular projective transformation 322
Singular space of a projective transformation 325
Skew-isomorphism 175
Skew-symmetric bilinear form 366
Skew-symmetric canonical form 378 380
Skew-symmetric matrix 86
Solution of linear homogeneous equations 68
Solution of linear homogeneous equations by determinants in the commutative case 84
Solutions of a set of equations 139
Space of points with no transform 358
Space, incidence 211
Space, linear 183 208
Space, projective 178
Space, projective number 170
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