Newman M. — Integral Matrices :: Электронная библиотека попечительского совета мехмата МГУ

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Newman M. — Integral Matrices

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Название: Integral Matrices

Автор: Newman M.

Аннотация:

Since integral matrices, or matrices over rings, are a huge subject which extends into many different areas of mathematics, this book concerns itself with matrix theory and its many applications. The primary discussion involves matrices over principal ideal rings.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 224

Добавлена в каталог: 14.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\Gamma$ -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 $\Gamma$       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 $\Gamma$       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 $\mu$       3
Congruence over field      62
Congruence over field of characteristic $\neq$ 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 $\Gamma$       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 $\Gamma^n$       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 $\Gamma$       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 $\Gamma(n)$       146
Index of $\Gamma_0(\mu)$       136
Index of $\Gamma_{r,s}(\mu)$       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 $\Gamma$       143
Normal subgroups of $\Gamma$ of genus 0      157
Normal subgroups of $\Gamma$ of level $\leq$ 5      145
Normal subgroups of $\Gamma$ of level 6      145 149
Normal subgroups of $\Gamma(2)$       149
Normalized vectors      84
Octahedral group      179
octahedron      99
Order of $G(\mu)$       115 135
Order of $G(\pi^l)$       115 135
Order of $GL(n, R/(\pi^l))$       114
Order of $\Gamma_0(\mu)/\Gamma(\mu)$       136
Order of $\Gamma_{r,s}(\mu)/\Gamma(\mu)$       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 $\neq$ 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 $G(\alpha, \beta)$       112 130
Rank      27
Rank of free subgroup of $\Gamma$       144
Rational canonical form      47
Real discrete representations of $\Gamma$       162
Real positive units      187
Reduced set of residues modulo $\mu$       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 $\mu$       131
Symplectic group      124
Symplectic modulo $\mu$       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

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