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| Авторизация |
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| Поиск по указателям |
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| Baer R. — Linear Algebra and Projective Geometry |
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| Предметный указатель |
Absorption law 312
Adjoint space 25—26
Adjunct space 36
Admissible, involutions of first and second kind 147
Admissible, projectivities 144
Annulet 172
Anti-automorphism 78
Anti-homomorphism 103
Anti-isomorphism 96
Anti-semi-linear transformation 99 190
Auto-projectivities, group of 52
Basis 13 265
Betweenness 223
Bilinear form 101
Canonical dual space 98
Center of a group 201
Center of a perspectivity 292
Centralizer, first 63 203
Centralizer, second 203
Characteristic two, criteria for Fano’s postulate 38 IV. 114 IV. 116
Class of a linear transformation 207
Collineation 62
Commutativity, criteria for, of the field of scalars III. 3. Proposition 2 67 Second 68 Postulate 71 III. 75—76 III. 87 IV. 106 IV. 108 IV. 114 IV. 132 IV. 141 IV. 143
Complement 12
Complementation principle 260
Complementation theorem 12
Conjugate numbers in fields 72
Containedness 8
Cross ratio 71—72
Crossed homomorphisms 248
Decomposition endomorphisms 169
Dedekind’s (or modular) law 9 259
Dependence of elements (vectors) 13
Dependence of points 41 264
Desargues’ theorem 266—267
Dilatation 53 57
DIMENSION 16 265
Direct sum 12
Dualities 32 95 310
Duality principle of projective geometry 100 263
Duality theorem 97
Euclidean fields 144
Euclidean fields, anti-isomorphisms of endomorpliism rings 192—193
Existence theorem for basis 14
Existence theorem for dualities 96
Existence theorem for polarities 159
Fano’s postulate 37
Field 7
Finiteness, criteria for, of rank II. 3. Corollary 1 26 II. 28 II. 30 IV. 96 IV. 97 IV. 97 IV. 103 IV. 108 IV. 111 V. 182 V. 189 V. 192 V. 193 VI. 243 VI. 250 VI. 252
Flock 3 303
Formally real fields 144
Forms, bilinear 101
Forms, linear 25
Forms, semi-bilinear 101
Function space [F,C] 19
Fundamental theorem of projective geometry, complement to second III. 4. Theorem 2 87
Fundamental theorem of projective geometry, First 44
Fundamental theorem of projective geometry, Second 68
Galois correspondence between a space and its adjoint space 28
Galois correspondence between a space and its group VI. 4. Theorem 4 227
Galois correspondence between a space and its ring 172—173
Galois correspondence between direct decomposition into points and maximal groups of involutions VI. App. I. Remark 1 244
Geometry defined by a bilinear form IV. 5. Remark 3 152
Group automorphism of endomorphism ring V. 4. Theorem 2 187
Group automorphism of full linear group 237
Group automorphism of full semi-linear group 256
Group homothetic 52
Group of a duality 144
Group of a hyperplane 292
Group of a linear manifold (survey) 63
Group of collineations 62
Group of involutions 237
Group of multiplications 52 63 246
Group, extended, of automorphisms of endomorphism ring 196
Harmonic set III. 4. Remark 5 76
Homothetic transformation 53 57
Hyperplane 19 264
Ideals 172
Idempotents 169
Imbedding theorem 268
inclusion 8
Independent elements (vectors) 13
Independent points 41 264
| Index of inertia (Sylvester) 130
Index of polarity 121
Induced isomorphisms of first kind of full linear group 229
Induced isomorphisms of first kind of full semi-linear group 249
Induced isomorphisms of second kind of full linear group 229
Induced isomorphisms of second kind of full semi-linear group 251
Intersection of subspaces 9
Involutions 144
Involutorial mappings 111
Isomorphism law 11
Isomorphism theorem for endomorphism ring V. 4. Theorem 1 183
Isomorphism theorem for full linear group 231
Isomorphism theorem for full semi-linear group 252
Isotropic subspaces 113
Isotropic subspaces, strictly 109 113
Kernel 168
Line 18 71 265
Linear anti-form 36
Linear dependence and independence 13
Linear form 25
Linear manifold 7
Linear mapping 91
Linear transformation 42
Maximal elements in partially ordered sets 310
Maximum principle of set theory 310
Multiplications, characterization of III. 1. Proposition 3 43
Multiplications, group of 52 63 246
Non-lsotropic subspaces 101 113
normalizer 219
Null systems and N-sub spaces 106
Nullity of a polarity 116
Nullity of an endomorphism 168
Ordering, algebraic, of a field 94 127
Ordering, projective, of a space 94
Orthogonal group 158
Orthogonal idempotents 169
Paired spaces 35
Pappus, postulate of 71
Pappus, property of 69
Partially ordered set 258 309
Pascal, theorem of 143
Pascalean polarity 139
permutations 309
Perspectivity 64 292
Plane 18 265
Point 18 260
Polarity, pole-polar relation 109
Positivity, domain of 93 127
Preservation of forms by transformations 151
Projection of aline from a point 91
Projectivity 40 310
Pythagoras, Theorem of 152
Quotient spaces 10
Rank formulas for a pair of subspaces 17—18
Rank formulas for a subspace and its dual 33
Rank of a subspace 16 265
Rank of an endomorphism 168
Regular rings 179
Ring of endomorphisms of a linear manifold 169
Self-duality theorem 97
Semi-automorphism 83
Semi-bilinear form 101
Semi-linear transformation 42
simplex 66
Singular automorphisms of full linear group 230
Singular automorphisms of full semi-linear group 247
Strictly isotropic 113
Structure theorem for endomorphism ring of linear manifolds 183
Structure theorem for full linear groups 229
Structure theorem for full semi-linear groups 247
Structure theorem for linear manifolds 16
Structure theorem for projective spaces 51
subspace 8
Sum of subspaces 9 259
Surveyof groups of a linear manifold 63
Sylvester’s theorem of inertia 129
Symmetrical forms 111
Symplectic group 155
Transitive groups 153
Translation 53 57
Uniqueness theorem for anti-semi-linear transformations 194
Uniqueness theorem for polarities 148 159
Uniqueness theorem for rank 14
Unitary group 158
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