|
Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
|
|
|
|
|
Newman M. - Integral Matrices |
|
|
Предметный указатель |
-equivalence 155
Arithmetic minimum 72 202
Arithmetically multiplicative functions 19
Ascending chain condition 4
Associate 2
Automorphs 124 178 196
Bound(s) for arithmetic minimum 73 75 95 202
Bound(s) for cofactors 207 208
Bound(s) for discriminant 101
Bound(s) for Hermite constant 203 204
Bound(s) for Hermite constant, generalized 214
Bound(s) for order of finite integral matrix group 175 177
Bound(s) for rank 189
box 96
Burnside problem 143
Canonical sets of generators and relations for 157
Cauchy - Binet theorem 25 26
Center(s) of GL(n,S), SL(n, S) 104
Center(s) of Sp(2n,R) 125
Central symmetry 90
Character of matrix representation 17
Characteristic polynomial 46
Chinese remainder theorem 8
Circulants 183
Class function 19
Class number 19 34 53 54 60 73 75 188 199 208
Classical modular group 138
Commutator subgroup of 140
Commutator subgroup of GL(n,R) 107
Commutator subgroup of SL(n,R) 108
Companion matrix 46
Complete set of residues modulo д 3
Compound 25
Congruence 56
Congruence groups 110 130
Congruence modulo 3
Congruence over field 62
Congruence over field of characteristic 2 63
Congruence over field, algebraically closed 64
Congruence over field, finite, of characteristic 2 68
Congruence over field, finite, of odd characteristic 66
Congruence over field, rational 71
Congruence over field, real 71
Congruence over Z 72
Convex sets 90
Coset representatives 119 136
Cyclotomic polynomials 183
Cylotomic units 187
Degree 43
Degree of matrix representation 171
Determinant of lattice 89
Determinantal divisors 25
Dihedral group 179
Diophantine analysis 37
Dirichlet's theorem on simultaneous diophantine approximation 98
Dirichlet's unit theorem 184
Discrete group 158 162
Divisor sums 19
Eigenvalue(s) 190
Eigenvalue(s), inequality 178 209
Eigenvectors 52
Elementary column operations 13
Elementary divisors 29
Elementary matrices 13
Elementary row operations 12 23
Elements of finite period of 142
Ellipsoids 93
Elliptic class numbers 153
Elliptic elements 154
EQUIVALENCE 12
Euclidean algorithm 43 126
Euclidean rings 7 23
Factorization of complex matrix 205 207
Finite exponent 169
Finite subgroups of GL(2, Z), GL(3,Z) 179 180 181
Finite subgroups of GL(4, Z) 181
Finitely generated abelian group 35
Finitely many conjugacy classes 170
Fixed points 155
Free group 141 143 158
Free product 139 162
Free rank 184
Frobenius normal form 47
Full cycle 182
Fully invariant subgroup 142
Fundamental region 155
Fundamental set 155
Fundamental theorem of geometry of numbers 92
Gaussian ring 5
General linear group 103
Generalized Hermite constant 214
Generalized n-cycle 191
Generalized permutation matrices 79
Generators of 141
Generators of 139
Generators of group of unit matrices 24
Generators of SL(n, R) 105
Generators of Sp(2n, R) 130
Genus 156
Gram - Schmidt process 83
Greatest common divisor 2
Group matrix of solvable group 195
Grusko's theorem 143
Hall - Ryser theorem 81
Hasse - Minkowski theorem 72
Hermite constant 202
Hermite normal form 15
Hermite normal form, uniqueness of 18
Hermite's method of reduction 73
Hermitian matrices 87
Hyperbolic elements 154
Ideal class 52
Incidence matrix 39
Inclusion theorem 120
INDEX 71
Index of 146
Index of 136
Index of 117
Inner product 83
Invariant factors 28
Irreducibility 164
Isometric circle 156
Isotropic vectors 84
| Jacobian 91
Jordan Matrix 48
Jordan normal form 48
Kronecker powers 174
Kronecker products 39 55
Kurosh subgroup theorem 141
Latimer - MacDuffee theorem 52
Lattice 88
Lattice basis 89
Least common multiple 110
Left equivalence 12
Left ideal 22
Length 83
Level 109 130 145 147
Linear forms theorem 96
Linear fractional transformations 138
Matrices of finite period 54
Matrices of period 2 54
Matrices over rings 11
Matrices, representation of 170
Minimal polynomial 46
Module basis 52
Modules 21
Multiples 25
Multiplicatively closed sets of nonassociates 6
Multiplicativity of Smith normal form 33
Natural homomorphism 109 177
Noncongruence groups 149
Nonderogatory matrix 46
Norm 4
Norm constant 214
Normal closure 142
Normal matrices 86
Normal subgroups of 143
Normal subgroups of of genus 0 157
Normal subgroups of of level 5 145
Normal subgroups of of level 6 145 149
Normal subgroups of 149
Normalized vectors 84
Octahedral group 179
octahedron 99
Order of 115 135
Order of 115 135
Order of 114
Order of 136
Order of 116
Order of GL(n,GF(q)) 114
Order of SL(n,GF(q)) 114
Order of Sp(2n, GF (q)) 125
Ordered fields 69
Orthogonal equivalence 79
Orthogonal equivalence over fields of characteristic 2 80
Orthogonal matrix 79
Orthogonal vectors 83
Orthogonality relationships for characters 171 172
Orthonormal basis 85
Parabolic class number 151 156
Parabolic element 147 157
Partitions 34
Peano - Jordan volume 91
Pell equation 191
Permutation equivalence 39
Permutation matrix 182
Positive definite matrices 71
Prime 5
Principal congruence group 109 130
Principal ideal rings 1
Projective general linear group 105
Projective special linear group 105
Proper degree 43
Proper euclidean ring 125
Quadratic form 56 201
Quotient group 112 130
Rank 27
Rank of free subgroup of 144
Rational canonical form 47
Real discrete representations of 162
Real positive units 187
Reduced set of residues modulo 9
Reducibility 164
Relative primality 3
Representation of cyclic group 182
Representation of cyclic group by forms 61
Right equivalence 12
Rings of complex numbers 212
Roots of unity 54
Schreier's theorem 144
Schur's lemma 165
Schur's theorem on unitary equivalence 86
Schwarz inequality 83
Similarity 41
Similarity over field 43
Similarity over Z 49
Similarity to block triangular matrix 50
Similarity to diagonal matrix 49
Simple elementary divisors 29
Skew normal form 57
Skew-Hermitian matrices 87
Skew-symmetric matrix 57
Smith normal form 26
Special linear group 103
Substitute for Dirichlet's theorem 119
Sums of squares in finite fields 66
Sylvester's law of inertia 69
Symmetric matrix 57
Symmetric modulo 131
Symplectic group 124
Symplectic modulo 131
Tetrahedral group 179
Totally positive units 187
Triple diagonal matrix 60
Unimodular matrices 12
Unique factorization 5
Unit sphere 93
Unitary equivalence 82
Unitary matrix 82
UNITS 2
Volume of ellipsoid 94
Volume of unit sphere 94
Volume under linear transformations 91
Weierstrass criterion 49
Witt's theorem 64 198
Z-module 52
|
|
|
Реклама |
|
|
|
|
|
|