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Gruenberg K.W. — Linear Geometry
Gruenberg K.W. — Linear Geometry

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Название: Linear Geometry

Автор: Gruenberg K.W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1977

Количество страниц: 212

Добавлена в каталог: 05.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Affine geometry      see “Geometry”
Affinity      42
Affinity, degenerate      70
angle      126 128
Annihilator      81
Annihilator, ideal      151
Annihilator, mapping      81 94
Anti-automorphism      120 122
Anti-isomorphism      84
Associative law for mapping multiplication      3
Associative law for matrix multiplication      73
Automorphism of euclidean geometry      14
Automorphism of field      56 58 65 123
Automorphism of Hilbert space      146
Automorphism of R-module      154
Automorphism of sesquilinear space      124
Automorphism of similarity euclidean geometry      144
Automorphism of vector space      66
Automorphism, groups for $\Gamma$, A, P, F      59
Axis of central collineation      48
Basis (base)      9
Basis (base) of torsion-free $\mathrm{F}[\mathrm{X}]$-module      163
Basis (base), cartesian      127 142 146
Basis (base), dual      80
Basis (base), standard of $\mathrm{F}[\mathrm{X}]^n$      168
Basis (base), standard of $\mathrm{F}^n$      12 13
Basis (base), standard of $\mathrm{F}^{m \times n}$      74
Bilinear form      89
Bilinear form, alternating      99
Bilinear form, degenerate      91 92
Bilinear form, negative definite      106
Bilinear form, orthosymmetric      97 101
Bilinear form, positive definite      106
Bilinear form, skew-symmetric      99 101
Bilinear form, symmetric      97 101
Bilinear polynomial      90
Canonical matrix, Jordan (classical)      167
Canonical matrix, rational      166
Cartesian basis      127 142 146
Center of (central) collineation      48 54 63 83
Center of affine polarity      111
Center of affine quadric      119
Center of perspective of two triangles      23
Center of perspectivity      48 65
Center of sphere      133
Central collineation      48 54 62 83
Central collineation, center of      see “Center”
Central collineation, hyperplane of      63
Centroid      48
Characteristic      2
Characteristic (Fano's Theorem)      40 111 115
Characteristic, field of      40 99
Classical (Jordan) canonical matrix      167
Classification of collineations      170
Coefficient space      50
Collineation      45 170
Collineation, central      see “Central”
Completeness of Hilbert space      147
Completion of affine quadric (to projective quadric)      117 118 120
Complexification of real bilinear form      124 146
Complexification of real vector space      14 58 112 134 136 140
Congruence of bilinear forms      89 90 103
Congruence of matrices      86 90 103
conic      111 114 120
Conic, action      116
Cono, representative      115
Coordinate row (homogeneous) of a projective point      47
Coordinate row of a vector      13
Coordinate row of an affine point      44
Coordinate system (homogeneous) for a projective geometry      46
Coordinate system for a euclidean geometry      129
Coordinate system for a vector space      13
Coordinate system for an affine geometry      44
Correlation      85 110 120
Correlation, degenerate      110
Coset (translated subspace)      15
Coset (translated subspace), dimension of      16
Coset (translated subspace), parallel      18
Coset (translated subspace), space of      67 154
Coset (translated subspace), subspace belonging to      16
Cross-ratio      132 133
Degenerate, affine polarity      111
Degenerate, affine quadric      119
Degenerate, affinity      70
Degenerate, bilinear form      91 92
Degenerate, correlation      110
Degenerate, null-polarity      110
Degenerate, polarity      110
Degenerate, projective quadric      112
Degenerate, projectivity      70
Degenerate, subspace (with respect to a bilinear form)      92 95
Desargue's Theorem (affine)      23
Desargue's Theorem (projective)      32 38 41 48 51 86
Desargue's Theorem, converse of      38
Desargue's Theorem, related to a division ring      39 40 48
Determinant      144
Dilatation      44 49 54 63 75
Dimension of a coset      16
Dimension of a projective geometry      30
Dimension of a vector space      10
Dimension of an affine geometry      16
Dimension, finite      9 15
Dimension, projective      30
Direct sum of submodules      155
Direct sum of subspaces      7 8 11 12 95 96 102 155
Distance on a coset      127
Distance on a euclidean space      125
Distance on a Hilbert space      146
Distance on a vector space      125
Distance, similar      131
Division ring      39 49 75
Dual basis      80
Dual configuration      84
Dual frame of reference      87 88
Dual geometry      86
Dual proposition      84
Dual space      80
Dual, self      171 172
Duality      85
Duality, principle of      84
Eigenspace      71 135 142 143
Eigenvalue      71 135 137 14
Eigenvector      71 135 140
Elementary divisors of a finitely generated F[X]-module      159 160
Elementary divisors of a linear mapping      166
Elementary divisors of a matrix      168 169
Elementary move      164 165
Elementary transformation      70
Embedding theorem      32 52 61 116 130
Equation of affine quadric      117
Equation of euclidean quadric      138
Equation of projective quadric      112
Equation, linear      49 79 82
Equivalence of matrices      77 165
Exchange Lemma      9
Exponent of commutative group      153
Family      2
Fano'a Theorem      40
Field      4 5
Field of characteristic      2 40 99 111 115
Field of gaussian numbers      14
Field of quotients      160
Field, ground      12
Finite dimensional vector space      9 15
Finite field      109 162 174
Finite geometry (affine)      20 29 38
Finite geometry (projective)      32 40 41 119 174
Form, Hermitian      122
Form, linear      80 101
Form, quadratic      100
Form, sesquilinear      121
Frame of reference for $\mathscr{P}(\mathrm{V})$ determined by a basis of V      46
Frame of reference for a euclidian geometry      129
Frame of reference for a projective geometry      46
Frame of reference for an affine geometry      43
Frame of reference standard for $\mathscr{A}(\mathrm{F}^{n+1})$      47
Frame of reference standard for $\mathscr{A}(\mathrm{F}^{n})$      43
Function      see “Mapping”
Gaussian number field      14
Generator of a projective quadric      114
Geometry, affine      35
Geometry, affine (generalized)      16
Geometry, affine, in $\mathscr{P}(\mathrm{V})$ determined by H      36 61 130
Geometry, determined in $\mathscr{P}(\mathrm{V})$ by H and D      132
Geometry, Euclidean      127
Geometry, projective      35
Geometry, projective (generalized)      29
Geometry, similarity euclidean      131
Geometry, “affine of dimension n over F”      22
Geometry, “projective of dimension n over F”      32
Greatest common divisor      161
Ground field      12
Group      4
Group, abelian (commutative)      4 150 160 163
Group, affine      59 75
Group, automorphism      59
Group, collineation (projective)      59
Group, commutative      see “Group abelian”
Group, general linear      59
Group, homomorphism of      59
Group, isomorphism of      59
Group, orthogonal      144
Group, permutation      4 62
Group, projective      see “Group collineation”
Group, rotation      4 144
Group, unitary      146
Harmonic, conjugate, (affine)      27
Harmonic, conjugate, (projective)      40
Harmonic, Constructive, (affine)      27
Harmonic, Constructive, (projective)      40 52
Harmonic, rango, (affine)      27
Harmonic, rango, (projective)      40 113 133
Hermitian form      122 124
Hermitian mapping      147
Hermitian matrix      124
hilbert      146
Hilbert space      146
Homogeneous (projective) coordinate row      47
Homogeneous (projective) linear equations      50
Homogeneous (projective) vector      22 30
Homomorphism of groups      59
Homomorphism of R-modules      154
Homomorphism of vector spaces      66
Hyperplane at infinity      36
Hyperplane in affine geometry      16
Hyperplane in projective geometry      30
Hyperplane of a central collineation      63
Ideal      152
Ideal, annihilator      151
Ideal, principal      152
Identity element of group      4
Identity element of ring      149
Identity mapping      2 3
Identity matrix      73
Image      2
Incidence propositions (affine)      19
Incidence propositions (projective)      31
Indecomposable submodule      159
Index notation      2
Infinite dimensional vector space      9 11 68 69 82 92 130 147
Integral domain      155 160
Intersection of cosets      16
Intersection of sets      3
Intersection of subspaces      7
Invariant configuration      170
Invariant factors of linear mapping      166
Invariant factors of matrix      168 169
Invariant factors of module      156 160 165
Invariant subspace      153
Inverse of a group element      4
Inverse of a mapping      3
Inverse of a matrix      73 74
Isomorphism of affine geometries      20 52
Isomorphism of bilinear spaces      89
Isomorphism of euclidean geometries      128 130
Isomorphism of fields      56
Isomorphism of groups      59
Isomorphism of modules      154
Isomorphism of projective geometries      31 52
Isomorphism of similarity euclidean geometries      131
Isomorphism of vector spaces      12
Isomorphism, anti-isomorphism      84
Isomorphism, linear isomorphism      66 91
Isomorphism, semi-linear isomorphism      56
Join (sum) of subspaces      7
Join of cosets      16
Jordan (classical) canonical matrix      167
Jordan canonical      107
Kernel of group homomorphism      60 62
Kernel of linear mapping      66
Kernel of module homomorphism      154
Kronecker delta      69 73
Length (norm) in euclidean space      125
Length (norm) in Hilbert spaee      146
Length of element in a principal ideal domain      161
Line at infinity      36 37
Line in affine geometry      16
Line, projective      30
Linear algebra      08 136
Linear automorphism      66
linear combination      6
Linear complex      110
Linear dependence      8
Linear equations      49 79 82
Linear form      80
Linear independence, over F      9
Linear independence, over F[X]      158
Linear isomorphism      12 66 91
Linear mapping      66
Linear mapping, $\sigma$-symmetric      135 140
Linear mapping, commuting      140 147
Linear mapping, similar      154
Linear mapping, trace of      75 83
Linear mapping, transpose of      83 93 169
Linear mapping, triangulable      140 147
Mapping (function)      2
Mapping (function) annihilator      81 94
Mapping (function), hermitian      147
Mapping (function), inverse      3
Mapping (function), normal      147
Mapping (function), one-one      2
Mapping (function), product of      2
Mapping (function), semi-linear      120
Mapping (function), unitary      147
Matrix      72
Matrix of bilinear form      90
Matrix of linear mapping      72
Matrix of quadratic form      102
Matrix, addition of      72
Matrix, alternating      103
Matrix, congruence of      86 103
Matrix, diagonal      104
Matrix, equivalence of      77 165
Matrix, hermitian      124
Matrix, identity      73
Matrix, inverse of      73 74
Matrix, invertible (non-singular)      74
Matrix, multiplication of      72
Matrix, nilpotent      74
Matrix, non-singular (invertible)      74
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