|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
C^n
|
|
gptkbp:centralTo
|
scalar matrices
|
|
gptkbp:compact
|
true
|
|
gptkbp:contains
|
gptkb:SL(n,_C)
gptkb:unitary_group_U(n)
gptkb:orthogonal_group_O(n,_C)
permutation matrices
diagonal matrices
|
|
gptkbp:definedIn
|
the group of n x n invertible matrices over the complex numbers
|
|
gptkbp:determinant
|
gptkb:SL(n,_C)
gptkb:C*
|
|
gptkbp:dimensions
|
n^2
|
|
gptkbp:field
|
complex numbers
|
|
gptkbp:fullName
|
general linear group of degree n over the complex numbers
|
|
gptkbp:hasConnection
|
true
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(n, C^n)
|
|
gptkbp:identityElement
|
identity matrix
matrix inverse
|
|
gptkbp:isAlgebraicGroup
|
true
|
|
gptkbp:isClassicalGroup
|
true
|
|
gptkbp:isComplexLieGroup
|
true
|
|
gptkbp:isDenseIn
|
M(n, C)
|
|
gptkbp:isGroupOfAutomorphisms
|
true
|
|
gptkbp:isGroupOfLinearTransformations
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isNonCompactLieGroup
|
true
|
|
gptkbp:isOpenSubsetOf
|
M(n, C)
|
|
gptkbp:isQuotientOf
|
gptkb:projective_general_linear_group_PGL(n,_C)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:isTopologicalGroup
|
true
|
|
gptkbp:notation
|
gptkb:GL(n,_C)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:relatedGroup
|
matrix multiplication
|
|
gptkbp:bfsParent
|
gptkb:GL(n,_C)
|
|
gptkbp:bfsLayer
|
7
|