|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
K^n
|
|
gptkbp:centralTo
|
scalar matrices
|
|
gptkbp:contains
|
orthogonal group
permutation matrices
diagonal matrices
|
|
gptkbp:definedIn
|
group of n x n invertible matrices over field K
|
|
gptkbp:determinantNonzero
|
true
|
|
gptkbp:dimensions
|
n^2
|
|
gptkbp:field
|
K
|
|
gptkbp:fullName
|
general linear group of degree n over K
|
|
gptkbp:hasConnection
|
true if K is algebraically closed
|
|
gptkbp:hasSubgroup
|
gptkb:Weyl_group
gptkb:maximal_torus
Borel subgroup
SL_n(K)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL n(K)
|
|
gptkbp:identityElement
|
identity matrix
matrix inverse
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isMatrixGroup
|
true
true if K = R or C
|
|
gptkbp:isNonAbelian
|
true for n = 1
true for n > 1
|
|
gptkbp:isQuotientOf
|
PGL_n(K)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSimple
|
false for n > 1
|
|
gptkbp:isTopologicalGroup
|
true if K is topological field
|
|
gptkbp:matrixSize
|
n x n
|
|
gptkbp:notation
|
gptkb:GL(n,_K)
gptkb:GL_n(K)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
finite if K is finite
product_{i=0}^{n-1} (|K|^n - |K|^i) if K is finite
|
|
gptkbp:relatedTo
|
gptkb:algebraic_geometry
differential geometry
number theory
representation theory
determinant
automorphism group of vector space
|
|
gptkbp:bfsParent
|
gptkb:Groupe_linéaire_général
|
|
gptkbp:bfsLayer
|
8
|