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| Авторизация |
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| Jacobson N. — Lectures in Abstract Algebra, Vol. 2 |
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| Предметный указатель |
Algebra 26 225
Algebra of linear transformations 36
Algebra, free 210—211
Algebra, Grassmann 211
Bases 15
Bases of infinite dimensional vector spaces 239
Bases, Cartesian 173
Bases, change of 42
Bases, complementary 53
Bases, matrix of 15
Bases, unitary 190
Bilinear forms 137
Bilinear forms, matrices of 138
Bilinear forms, non-degenerate 140
Burnside’s Theorem 276
Canonical matrices, classical 73 94
Canonical matrices, Jordan 70 93
Chain conditions 28
Characteristic polynomial 98 103
Characteristic roots 104
Characteristic roots of real symmetric matrices 180
Characteristic spaces 182
Characteristic vector 100 186
Cogredience (of matrices) 149
Commutative sets of linear transformations 133—135
Complete reducibility of a single linear transformation 129
Complete reducibility of sets of linear transformations 124
Complete reducibility, orthogonal 177
Composition series 120
Conjugate space 52
Conjugate space of infinite dimensional vector space 244
Cyclic linear transformations 69
Cyclic linear transformations, elementary divisors 73
Decomposability of a single linear transformation 129
Decomposability of sets of linear transformations 122
Dense rings of linear transformations 259—264
Dimensionality of free modules 89
Dimensionality of infinite dimensional vector spaces 241 244
Dimensionality of vector spaces 10 14
Direct product of linear transformations 203
Direct product of spaces 201
Direct sum of submodules 85
Direct sum of subspaces 30
Duality of infinite dimensional vector spaces 253
Duality of vector spaces and conjugate spaces 54
Elementary divisors 73 94
Endomorphisms of cyclic module 106
Endomorphisms of finitely generated module for principal ideal domain 108
Exponential function 197
Extension of field of vector space 221
Factor space 25
Finitely generated commutative groups 88
Frobenius theorem 102 111
Gaussian domain 101
General density theorem 274
Geometry Euclidean 172
Geometry unitary 190
Group, full linear 46
Group, unitary 191
Hamilton — Cayley theorem 101
Ideals in ring of linear transformations 230 232 256
Ideals, elementary divisor ideals 94
Ideals, invariant factor ideals 92
Ideals, order ideal 85
Invariant factors 84
Irreducible algebras of linear transformations 274
Irreducible set of endomorphisms 259
Irreducible set of linear transformations 116
Isomorphisms in infinite dimensional vector spaces 264
Isomorphisms of rings of linear transformations 233
Jordan — Holder theorem 127
Kronecker delta 17
Kronecker product of algebras 225
Kronecker product of infinite dimensional vector spaces 256
Kronecker product of linear transformations 211
Kronecker product of matrices 213
Kronecker product of vector spaces 208
Krull — Schmidt theorem 127
Lattices 26
Lattices, complemented 27 125
Lattices, modular 27
Linear dependence 10
Linear equations 47
Linear function 32 51
Linear transformations commuting with a given one 110
Linear transformations in right vector spaces 49
Linear transformations induced in invariant subspace and factor space 117
Linear transformations, addition of 32
Linear transformations, analytic functions of 194
Linear transformations, definition 32
Linear transformations, matrix of 36—37
Linear transformations, minimum polynomial of 65
Linear transformations, normal 184
Linear transformations, nullity of 44
Linear transformations, orthogonal 178
Linear transformations, polar factorization 188 192
Linear transformations, power series in a linear transformation 195
Linear transformations, product of 34
| Linear transformations, rank of 44
Linear transformations, semi-definite 186
Linear transformations, skew 178
Linear transformations, symmetric 178
Linear transformations, transpose of 56 142
Linear transformations, unitary 191
Matrices 15 18
Matrices in infinite dimensional vector spaces 243
Matrices of bases 15
Matrices of bilinear forms 138 149
Matrices of linear transformations 37
Matrices of transpose 58
Matrices, addition of 39
Matrices, column rank of 22
Matrices, elementary divisors of 94
Matrices, elementary matrices 19 82
Matrices, equivalence of 42 79
Matrices, Hermitian 150 191—192
Matrices, invariant factors of 84
Matrices, multiplication of 39
Matrices, non-singular 16
Matrices, normal 185
Matrices, normal form of 84
Matrices, orthogonal 175
Matrices, row rank of 22
Matrices, similarity of 43
Matrices, symmetric 179
Minimum polynomial 65 98
Minimum polynomial, degree of 69
Modules 7
Modules, cyclic 85
Modules, equivalence of 8
Modules, factor 88
Modules, finitely generated 8 76 85
Modules, free 8 76
Modules, generators of 8
Modules, submodule 7
Partially ordered set 26
Primary components 130—132
Product group of vector spaces 200
Projection 60
Projection, orthogonal 60
Projection, supplementary 60
Rank in infinite vector spaces 256
Rank of a set of vectors 22
Rank of linear transformations 44
Rank, column rank of matrices 22
Rank, determinantal rank 23
Rank, row rank of matrices 22
Reducibility of a single linear transformation 128
Reducibility of sets of linear transformations 116
Ring of linear transformations, anti-automorphism 267
Ring of linear transformations, automorphism 237
Ring of linear transformations, center of 114
Ring of linear transformations, finite topology in 248
Ring of linear transformations, isomorphisms 233 266
Ring of linear transformations, left ideals in 230
Ring of linear transformations, right ideals in 232
Ring of linear transformations, simplicity 227
Ring of linear transformations, two-sided ideals in 256
Rotation 179
Scalar products 148
Scalar products, alternate 160
Scalar products, hermitian 150
Scalar products, non-degenerate 151
Scalar products, totally regular 167
Scalar products, weakly hermitian 268
Schmidt’s orthogonalization process 174
Schur’s lemma 271
Subspaces of infinite dimensional vector spaces 242
Subspaces, cyclic 66
Subspaces, direct sum 30
Subspaces, independent 28
Subspaces, invariant 66 115
Subspaces, isotropic 151
Subspaces, total 251
Sylvester’s theorem 156
Tensors 213
Tensors, contraction of 215
Tensors, skew symmetric 218
Tensors, symmetry classes 217
Topological space 248
Trace of a matrix 99 103 216—217
Transitivity 272
Vector spaces, abstract (finite dimensional) 3
Vector spaces, conjugate space of 53
Vector spaces, cyclic 69
Vector spaces, dimensionality of 10 14
Vector spaces, infinite dimensional 238
Vector spaces, Kronecker product of 208
Vector spaces, right 6
Vector spaces, two-sided 204
Vectors, linear dependence 10
Vectors, order of 67
Vectors, product 1
Vectors, scalar product 1
Vectors, sum 1
Witt’s Theorem 162
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