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| Авторизация |
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| Поиск по указателям |
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| Greub W.H. — Linear Algebra |
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| Предметный указатель |
A  -gradation 165
Abelian group 2
Adjoint mapping 204
Adjoint mapping, matrix 111
Affine coordinates 280
Affine coordinates, coordinate-system 280
Affine coordinates, equivalent quadrics 293
Affine coordinates, mapping 281
Affine coordinates, space 279
Affine coordinates, subspace 281
Algebra 139
Algebra of linear transformations 141
Algebra of quaternians 321
Algebraic number 161
Almost finite gradation 166
Alternative theorem 86
angle 183
Anticommutative graded algebra 171
Antiderivation 149
Associative algebra 140
Associativity (groups) 1
Augmented matrix 88
Barybicentric coordinates 208
Basis 11
Basis transformation 91
BesseFs-inequality 189
Bicommutant 403
Bilinear function 63
Binomial formula 171
Boundaries 173
Bounded linear transformation 201
Canonical injection 23
Canonical injection, involution 171
Canonical injection, projection 26
Canonical injection, projection (group) 2
Cauchy-criterion 203
Cayley — Hamilton theorem 399
Center 283
Center of an algebra 150
Chain 4
Chain, rule 341
Characteristic coefficients 118
Characteristic coefficients, equation 116
Characteristic coefficients, polynomial 118 373
Characteristic coefficients, polynomial of a matrix 120
Characteristic coefficients, zero (field) 3
Co-dimension 36
Coboundaries 174
Cocycles 174
Coefficient field 5
Cofactor 111
Cohomology space 174
Column-vectors 82
Commutant 402
Commutative algebra 140
Commutative algebra, (group) 2
Compatible gradations 165
Complementary subspace 26
Complete normed linear space 203
Complex vector space 6
components 11
composition 18
Cone with vertex 285
Conjugate determinant-function 313
Conjugate determinant-function, linear transformations 394
Conjugate determinant-function, principal axes 300
Conjugation 312
Connecting mapping 174
continuous curve 232
Continuously differentiable curve 232
Contragradient basis-transformations 92
Convergent sequence 203
Convex subsets 270
Coset (group) 2
Cosine-theorem 184
Covarient components 199
Cramer’s solution formula 112
Cross product 194
Cycles 173
Cyclic space 383
Deformable basis 132
Degree of a homogeneous linear of a polynomial 339 431
Degree of a homogeneous linear, mapping 163
Degree of a homogeneous linear, of nilpotcncy 153
DeMoivre’s formula 242
Derivation 147
Derivation, p-derivation 148
Derived algebra 143
Determinant of a linear transformation 102
Determinant of a linear transformation of an n x n matrix 106
Determinant-function 98
Diagonal mapping 56
Difference vector 279
Difference vector, space 279
Differentiable curve 232
Differential algebra 178
Differential algebra, operator 173
Differential algebra, space 173
Differentiation map 341
DIMENSION 32
Direct sum (external) 55
Direct sum (external), (internal) 24
Distance 189
Distributive law (field) 3
Division-algebra 321
Divisor 345
Dual bases 76
Dual bases, determinant-function 109
Dual bases, differential spaces 174
G-graded algebra 169
G-graded algebra, differential algebra 178
G-graded algebra, factor space 164
G-graded algebra, subalgebra 170
G-graded algebra, subspace 163
G-graded algebra, vector space 162
General linear group 53
General linear group, orthogonal group 223
Generalized eigenspaces 375
Generator 383
Ggraded spaces 174
Ggraded spaces, Eigen-space 211
Ggraded spaces, Eigenvalue 116
Ggraded spaces, Eigenvalues of a matrix 120
Ggraded spaces, Eigenvector 116
Ggraded spaces, Elementary transformation 94
Ggraded spaces, Elements of a matrix 82
Ggraded spaces, Ellipse 292
Ggraded spaces, Endomorphism 139
Ggraded spaces, Entries of a matrix 82
Ggraded spaces, Equilateral simplex 283
Ggraded spaces, Equivalent matrices 97
Ggraded spaces, Euclid algorithm 344 352
Ggraded spaces, Euclidean space 181 282
Ggraded spaces, Euler — Po incare characteristic 180
Ggraded spaces, Exact sequence 45
Ggraded spaces, Exchange theorem of Steinitz 16
Ggraded spaces, Expansion-formula 113
Ggraded spaces, Extension field 3
Ggraded spaces, Factor algebra 144
Ggraded spaces, Field 3
Ggraded spaces, Fitting decomposition 378
Ggraded spaces, Fore-cone 270
Ggraded spaces, formula 180
Ggraded spaces, Function 1
Ggraded spaces, group 3
Ggraded spaces, mappings 67
Ggraded spaces, sequence of differential spaces 174
Ggraded spaces, set 2
Ggraded spaces, space 29
Ggraded spaces, spaces 64
| Ggraded spaces, vectors 28
Graded space 162
Gram determinant 192 314
Greatest common divisor 346
Greatest common divisor, lower bound 4
Group 1
Group of degrees 162
Group of linear automorphisms 53
Group of permutations 2
Hadamard’s inequality 198
Hermitian function 309
Hermitian function, matrix 310
Homogeneous linear mapping 163
Homogeneous linear mapping, system of linear equations 85
Homogeneous linear mapping, vectors 162
Homology algebra 178
Homology algebra, space 173
Homomorphism of algebras 139
Homomorphism of algebras of differential algebras 178
Homomorphism of algebras of differential spaces 173
Homomorphism of algebras of exact sequences 47
Homomorphism of algebras of groups 2
Homothetic linear transformation 223
Homotopy operator 179
Hyperbola 292
Hyperplane 281
Ideal 143
Identification 55
Identity element 1
Im^ge space 41
Indefinite bilinear function 249
Indefinite bilinear function of a bilinear function 252 432
Indefinite bilinear function, of a pseudo — Euclidean space 264
Induced basis 75
Induced basis, orientation 128
Infinite-dimensional vector space 32
Inhomogeneous system of linear, equations 85
Inner product 181
Inner product, product space 181
Instantaneous axis 239
Integration operator 343
Intersection 23
Intersection, number 132
Inverse isomorphism 17
Inverse matrix 90
Involution 18
Irreducible algebra 156
Irreducible algebra, polynomial 345
Irreducible algebra, space 54 388
Isometric linear mapping 220
Isomorphic 17
Isomorphism of exact sequences 47
Jacobi identity 151
Jordan canonical matrix 391
Kernel 41
Kronecker symbol 75
Lattice 4
Leading coefficient 339
Least common multiple 346
Least common multiple, upper bound 4
Left ideal 143
Left ideal, inverse of a linear mapping 52
Leibniz formula 147
Lie algebra 151
Light-cone 264
Light-cone, vector 264
Linear automorphism 17
Linear automorphism, closure 23
Linear automorphism, combination 8
Linear automorphism, function 16
Linear automorphism, isomorphism 17
Linear automorphism, mapping 16
Linear automorphism, transformation 17
Linearly dependent vectors 9
Linearly dependent vectors, independent vectors 10
Linearly dependent vectors, ordered elements 4
Lorenz transformation 275
Lower bound 4
Lower bound, triangular matrix 90
Mapping 1
Matrix 82
Metric normal-form 30
Metrically equivalent quadrics 302
Minimum polynomial 357
Minkowsky-space 275
Minor 113
Monic polynomial 339
Monomial polynomial 339
Multiple 345
Multiplication operator 140
Multiplication operator, n-dimensional affine space 279
Multiplication operator, n-space over 7
Neighbourhood 38
Nilpotent element 153
Nilpotent element, linear transformation 121 406
Nilpotent element, part 365
Non-degenerate bilinear function 63
Non-trivial linear relation 9
Norm of a vector 181 310
Norm-function 200
Norm-topology 201
Normal form of a matrix 94
Normal form of a matrix, form of a quadric 290
Normal form of a matrix, linear transformation 207 316
Normal-vector 299
Normed determinant-function 191
Normed determinant-function, linear space 200
Nullspaces 63
Opposite algebra 140
Orientation 127
Orientation, preserving 127
Oriented angle 191
Origin 280
Orthocroneous transformation 275
Orthogonal basis 186
Orthogonal basis, complement 66 188
Orthogonal basis, matrix 188
Orthogonal basis, projection 189 214
Orthogonal basis, vectors 66 182
parabola 292
Parallel affine subspaces 281
Parallelogram-identity 245 1—
Parallelogram-identity, parameter group 237
Partially ordered set 4
Past-cone 270
Pauli-matrices 332
Poincare series 166
Point 279
Polar subspace 292 4
Polar subspace, function, . 150
Polar subspace, U, Polynomial, . 140
Positive basis 127
Positive basis, definite 248
Positive basis, definite Hcrmitian function 309
Positive basis, gradation 162
Positive basis, selfadjoint transformation 213
Positive basis, semidcfinite symmetric bilinear, function 248
Positive basis, vector 280
Prime polynomial 345
Principal axes 300
Principal axes, minors 114
Product (algebra) 139
Product (algebra) of matrices 89
Projection operator 59
Proper rigid motion 284
Proper rigid motion, dimensional parallelepiped 192
Proper rigid motion, homology space 176
Proper rigid motion, p-th Betti number 177
Proper rigid motion, rotation 224
Pseudo — Euclidean rotation 272
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