|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
R^n
|
|
gptkbp:application
|
gptkb:geometry
control theory
differential geometry
dynamical systems
group theory
physics
representation theory
linear algebra
automorphism groups
symmetry groups
|
|
gptkbp:centralTo
|
scalar matrices with nonzero real entries
|
|
gptkbp:connects
|
false
|
|
gptkbp:contains
|
gptkb:special_linear_group_SL(n,_R)
gptkb:orthogonal_group_O(n)
diagonal matrices with nonzero entries
|
|
gptkbp:definedIn
|
the group of n x n invertible matrices with real entries
|
|
gptkbp:determinant
|
det: GL(n, R) → R\\{0}
|
|
gptkbp:dimensions
|
n^2
|
|
gptkbp:field
|
R
|
|
gptkbp:fullName
|
general linear group of degree n over the real numbers
|
|
gptkbp:hasSubgroup
|
gptkb:GL(n,_C)
gptkb:SO(n)
gptkb:SL(n,_R)
O(n)
diagonal matrices
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(n, R)
|
|
gptkbp:identityElement
|
matrix inverse
n x n identity matrix
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:nonCompact
|
true
|
|
gptkbp:notation
|
gptkb:GL(n,_R)
|
|
gptkbp:numberOfConnectedComponents
|
2
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite
|
|
gptkbp:realPointsOf
|
GL(n, -)
|
|
gptkbp:specialSubgroup
|
gptkb:SL(n,_R)
|
|
gptkbp:topology
|
open subset of R^{n^2}
|
|
gptkbp:bfsParent
|
gptkb:GL(n,_C)
gptkb:general_linear_group_GL(n,_R)
gptkb:O(n,_R)
gptkb:SL(n,_R)
|
|
gptkbp:bfsLayer
|
7
|