|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Gruenberg K.W., Weir A.J. — Linear Geometry |
|
|
|
| Предметный указатель |
Infinite dimensional vector space 9 11 5 7 8) 68 69 2 4 9) 82 3 5 6) 92 2 3) 130 147
Integral domain 155 (exx. 1 3) 160
Intersection of cosets 16
Intersection of sets 3
Intersection of subspaces 7
Invariant configuration 170ff
Invariant factors of linear mapping 166
Invariant factors of matrix 168 169
Invariant factors of module 156 160 165
Invariant subspace 153
Inverse of a group element 4
Inverse of a mapping 3 (ex. 1)
Inverse of a matrix 73 74
Isomorphism ,semi-linear isomorphism 56
Isomorphism of affine geometries 20ff 62ff
Isomorphism of bilinear spaces 89
Isomorphism of euclidean geometries 128 130
Isomorphism of fields 56
Isomorphism of groups 59
Isomorphism of modules 154
Isomorphism of projective geometries 31 52ff
Isomorphism of similarity euclidean geometries 131
Isomorphism of vector spaces 12
Isomorphism, anti-isomorphism 84
Isomorphism, linear isomorphism 66 91
Join (sum) of subspaces 7
Join of cosets 16
Jordan (classical) canonical matrix 167
Ker f, kernel of f 66
Kernel of group homomorphism 60 62
Kernel of linear mapping 66
Kernel of module homomorphism 154
Kronecker delta 69 (ex. 6) 73
Length (norm) in euclidean space 125
Length (norm) in Hilbert space 146
Length of element in a principal ideal domain 161 (exx. 5 7)
Line at infinity 36 37
Line in affine geometry 16
Line, projective 30
Linear algebra 68 136
Linear automorphism 66
linear combination 6 (ex. 5)
Linear complex 110 (ex. 4)
Linear dependence 8ff
Linear equations 49ff 79ff 82
Linear form 80ff
Linear independence over F 9
Linear independence over F[X] 158
Linear isomorphism 12 66 91
Linear mapping 66
Linear mapping,  -symmetric 135 140
Linear mapping, commuting 140 (ex. 3) 147
Linear mapping, similar 154
Linear mapping, trace of 75 (exx. 8 9) 83
Linear mapping, transpose of 83 (exx. 7 8) 93 169
Linear mapping, triangulable 140 (ex. 3) 147
m(X), minimum polynomial 151
Mapping (function) 2
Mapping, annihilator 81 94
Mapping, hermitian 147 (ex. 6)
Mapping, inverse 3 (ex. 1)
Mapping, linear see "Linear mapping"
Mapping, normal 147 (ex. 6)
Mapping, one-one 2
Mapping, product of 2
Mapping, semi-linear 120
Mapping, unitary 147 (ex. 6)
Matrix 72ff
Matrix of bilinear form 90
Matrix of linear mapping 72
Matrix of quadratic form 102
Matrix, addition of 72
Matrix, alternating 103
Matrix, congruence of 86 103ff
Matrix, diagonal 104
Matrix, equivalence of 77 165
Matrix, hermitian 124 (ex. 2)
Matrix, identity 73
Matrix, inverse of 73 74
Matrix, invertible (non-singular) 74
Matrix, Jordan canonical 167
Matrix, multiplication of 72
Matrix, nilpotent 74
Matrix, non-singular (invertible) 74
Matrix, orthogonal 79 (exx. 2 3) 143
Matrix, rational canonical 166
Matrix, similarity of 79 166ff
Matrix, skew-symmetric 79 (exx. 1 3) 101
Matrix, symmetric 77 101
Matrix, transposed 77
Matrix, triangular 108 109 140 147
Matrix, unitary 146
Matrix, zero 72
Metric 125
Mid-point 29
Minimum polynomial of linear mapping 151
Minimum polynomial of matrix 168 169
Minkowski's inequality 129 (ex. 2)
Module 150
Module, cyclic 153
Module, finitely generated 153
Module, torsion 152 155 2) 165
Module, torsion-free 152 163 165 3)
M|K, module of cosets of K 154
n-tuple 2
n-tuple, ordered 2
Nilpotent matrix 74 (ex. 4)
Non-Desarguesian projective plane 39 48
Norm (length) in euclidean space 125
Norm (length) in Hilbert space 146
Normal mapping 147 (ex. 6)
Normal to a plane 134 (ex. 7)
Null-polarity 110
Order of (commutative) group 153 (ex. 4)
Order of general linear group 62 (ex. 3)
Orientation 144
Origin of affine frame of reference 43
Orthogonality 93ff 126 137 146
Orthogonality (anticipated) 51
Orthosymmetry 97 101 (ex. 122
Pappus' Theorem, (affine) 25
Pappus' Theorem, (projective) 39 40 51 88
Paraboloid 119
parallel 18
Parallelogram 37 64
Parallelogram, law 125
Pencil of lines 86 (ex. 3) 87
Pencil of planes 86 (ex. 3) 87
Permutation 4
Perpendicular 133 134
Perspective, axis of 38
Perspective, center of 23
Perspective, triangles in, from a point 23
| Perspectivity 48 (exx. 6—8) 49 65
Plane in affine geometry 16
Plane, projective 30
Point at infinity 36
Point in affine geometry 16
Point, projective 30
Polarity 110 113 3 4 7 8 16 17)
Polarity, affine 111 (exx. 5 6) 120
Polarity, definite 132
Polynomials, vector space of 6
Positive definite, hermitian form 123
Positive definite, symmetric bilinear form 106
Pr P, projective (collineation) group on P 59
Principal ideal 152
Principal ideal, domain 160 161
Projection 70 (ex. 9) 71
Projective geometry see "Geometry"
Projective space 30
Projectivity 45ff 88
Projectivity, degenerate 70ff
Pythagoras' theorem 100
Quadrangle 40 84
Quadratie form 100 101
Quadratie polynomial 100ff 108 111ff 117
Quadric, affine 116ff
Quadric, euclidean 134ff
Quadric, projective 111ff
Quadrilateral 84
Quaternion algebra (over  ) 75 (ex. 7) 101
Radius of sphere 133 (ex. 3)
Range of points 86 (ex. 3) 87
Rank of affine quadric 119
Rank of bilinear form 91
Rank of linear mapping 76ff 94
Rank of matrix (including row and column) 77
Rank of projective quadric 112
Rank of sesquilinear form 122
Rank of torsion-free F[X]-module 163
Rational canonical matrix 166
Reflexion 143 145
Relativity 107
Representative cone 115
Ring 149ff
Rotation 143 145 2 3)
Rotation group 4 144
S(V), semi-linear automorphisms of V 59
scalar 5
Schwarz's inequality 126
Segre symbol 170
Self-polar simplex 115 (ex. 15)
Semi-linear isomorphism 56
Semi-linear mapping 120
SEQUENCE 2
Sequence, ordered 2
Sesquilinear for, orthosymmetric 122
Sesquilinear form 121ff
Sets 1
Sets, equality of 2
Sf, the image of S under f 2
Signature 106 108
Similarity of distances 131
Similarity of linear mappings 154
Similarity of matrices 79 166ff
Simplex of reference 46
Skew elements in projective geometry 30
Skew lines in affino goometry 20
Space of cosets 67 154
Space time 107
Space, alternating (symplectic) 99 102ff
Space, bilinear 89
Space, coefficient 50
Space, dual 80
Space, eigen 71 (ex. 4) 135
Space, Euclidean 107 125ff
Space, Hilbert 146ff
Space, metric 125
Space, normed 125
Space, orthogonal (symmetric) 98 105ff
Space, projective 30
Space, skew-symmetric 99
Space, symmetric (orthogonal) 98 105ff
Space, symplectic (alternating) 99 102ff
Space, vector 5ff
Sphere 133 (exx. 3 4)
Split product of groups 60 144
Standard basis of ![$F[X]^n$](/math_tex/8c00c93bc7afc04ddad728c954a4c44b82.gif) 168
Standard basis of  12 (ex. 9) 13
Standard basis of  74 (ex. 2)
Subgeometry of affine geometry 16
Subgeometry of euclidean geometry 127
Subgeometry of projective geometry 30
Subgeometry of similarity euclidean geometry 131
Subgroup 4 59ff 144ff
Subgroup, Sylow 163 (ex. 13)
Submodule 153ff
Subring 149
subspace 6ff
Subspace, belonging to a coset 16
Subspace, direct sum of 7
Subspace, invariant 153
Subspace, spanned (generated) by a set 7
Subspace, sum (join) of 7
Subspace, translated see "Coset"
Sylvester's law of inertia 106
Tangent to a projective quadric 114 (exx. 9—11)
Torsion element 152 155
Torsion module see "Module"
Torsion-free F[X]-module 163 165 3)
Tr A, translation in A 59
Tr F, translations on V 59
Trace mapping 75 (exx. 8 9) 83
Translation group (in A and in V) 59
Translation in affine geometry 42 49 54 63 70
Translation in vector space 42
Transpose of linear mapping see "Linear mapping"
Transpose of matrix 77
Transvection 70 (ex. 11)
triangle 23
Triangle, diagonal point 40
Triangle, inequality 125
Union of sets 3
Unique factorization domain 160 161
Unit point of a projective frame of reference 46
Vector 5
Vector space 5ff
Vector space, dimension of 10ff
Vector space, finite dimensional 9
Vector, eigen see "Eigenvector"
Vector, homogeneous 22ff 30
V|K, space of cosets of K 67
Wedderburn's Theorem 39
Zorn's lemma 178 (solution of ex. 6 of § 4.6)
[S], subspace spanned by S 7
{x,y,...}, the set consisting of x,y,... 2
|
|
|
| Реклама |
|
|
|
|
|
О проекте