 -derivation 148
1-parameter group 237
A  -gradation 165
Abelian group 2
Adjoint mapping 204
Adjoint matrix 111
Affine coordinate-system 280
Affine coordinates 280
Affine equivalent quadrics 293
Affine mapping 281
Affine space 279
Affine 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
Bessel's-inequality 189
Bicommutant 403
Bilinear function 63
Binomial formula 171
Boundaries 173
Bounded linear transformation 201
Canonical injection 23
Canonical involution 171
Canonical projection 26
Canonical 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 equation 116
Characteristic polynomial 118 373
Characteristic polynomial of a matrix 120
Characteristic zero (field) 3
Co-dimension 36
Coboundaries 174
Cocycles 174
Coefficient field 5
Cofactor 111
Cohomology space 174
Column-vectors 82
Commutant 402
Commutative (group) 2
Commutative algebra 140
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 linear transformations 394
Conjugate 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 mapping 163
Degree of a polynomial 339
Degree of nilpotency 153
DeMoivre's formula 242
Derivation 147
Derived algebra 143
Determinant of a linear transformation 102
Determinant of an  matrix 106
Determinant-function 98
Diagonal mapping 56
Difference space 279
Difference vector 279
Differentiable curve 232
Differential algebra 178
Differential operator 173
Differential space 173
Differentiation map 341
DIMENSION 32
Direct (internal) 24
Direct sum (external) 55
Distance 189
Distributive law (field) 3
Division-algebra 321
Divisor 345
Dual bases 76
Dual determinant-function 109
Dual differential spaces 174
Dual G-graded spaces 174
Dual mappings 67
Dual spaces 64
Eigen-space 211
Eigenvalue 116
Eigenvalues of a matrix 120
Eigenvector 116
Elementary transformation 94
Elements of a matrix 82
ellipse 292
Endomorphism 139
Entries of a matrix 82
Equilateral simplex 283
Equivalent matrices 97
Equivalent vectors 28
Euclid algorithm 344 352
Euclidean space 181 282
Euler — Poincare characteristic 180
Euler — Poincare formula 180
Exact sequence 45
Exact sequence of differential spaces 174
Exchange theorem of Steinitz 16
Expansion-formula 113
Extension field 3
Factor algebra 144
Factor group 3
Factor set 2
Factor space 29
Field 3
Fitting decomposition 378
Fore-cone 270
Function 1
G-graded algebra 169
G-graded differential algebra 178
G-graded factor space 164
G-graded subalgebra 170
G-graded subspace 163
G-graded vector space 162
General linear group 53
General orthogonal group 223
| Generalized eigenspaces 375
Generator 383
Graded space 162
Gram determinant 192 314
Greatest common divisor 346
Greatest 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 matrix 310
Homogeneous linear mapping 163
Homogeneous system of linear equations 85
Homogeneous vectors 162
Homology algebra 178
Homology space 173
Homomorphism of algebras 139
Homomorphism of differential algebras 178
Homomorphism of differential spaces 173
Homomorphism of exact sequences 47
Homomorphism of groups 2
Homothetic linear transformation 223
Homotopy operator 179
Hyperbola 292
Hyperplane 281
Ideal 143
Identification 55
Identity element 1
Image space 41
Indefinite bilinear function 249
Index of a bilinear function 252
Index of a pseudo-Euclidean space 264
Induced basis 75
Induced orientation 128
Infinite-dimensional vector space 32
Inhomogeneous system of linear equations 85
Inner product 181
Inner 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 polynomial 345
Irreducible 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 upper bound 4
Left ideal 143
Left inverse of a linear mapping 52
Leibniz formula 147
Lie algebra 151
Light-cone 264
Light-cone-vector 264
Linear automorphism 17
Linear closure 23
linear combination 8
Linear function 16
Linear isomorphism 17
Linear mapping 16
Linear transformation 17
Linearly dependent vectors 9
Linearly independent vectors 10
Linearly ordered elements 4
Lorenz transformation 275
Lower bound 4
Lower 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
N-dimensional affine space 279
n-space over 7
Neighbourhood 38
Nilpotent element 153
Nilpotent linear transformation 121 406
Nilpotent 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 quadric 290
Normal linear transformation 207 316
Normal-vector 299
Normed determinant-function 191
Normed 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 complement 66 188
Orthogonal matrix 188
Orthogonal projection 189 214
Orthogonal vectors 66 182
p-th Betti number 177
p-th dimensional parallelepiped 192
p-th homology space 176
parabola 292
Parallel affine subspaces 281
Parallelogram-identity 245
Partially ordered set 4
Past-cone 270
Pauli-matrices 332
Poincare series 166
Point 279
Polar subspace 292
Polynomial 340
Polynomial function 350
Positive basis 127
Positive definite 248
Positive definite Hermitian function 309
Positive gradation 162
Positive selfadjoint transformation 213
Positive semidefinite symmetric bilinear function 248
Positive vector 280
Prime polynomial 345
Principal axes 300
Principal minors 114
Product (algebra) 139
Product of matrices 89
Projection operator 59
Proper rigid motion 284
Proper rotation 224
Pseudo-Euclidean rotation 272
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