|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
R^n
|
|
gptkbp:application
|
control theory
differential geometry
physics
representation theory
linear algebra
|
|
gptkbp:centralTo
|
scalar matrices with nonzero real entries
|
|
gptkbp:connectedComponent
|
matrices with positive determinant
|
|
gptkbp:definedIn
|
the group of n x n invertible matrices with real entries
|
|
gptkbp:determinant
|
SL_n(R)
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:SO(n)
gptkb:GL_n(C)
O(n)
SL_n(R)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL n(R)
|
|
gptkbp:identityElement
|
identity matrix
matrix inverse
|
|
gptkbp:isConnectedFor
|
n=1
|
|
gptkbp:isNonAbelian
|
n>1
|
|
gptkbp:isNotConnectedFor
|
n>1
|
|
gptkbp:isSimple
|
n=1
|
|
gptkbp:notation
|
gptkb:GL_n(R)
|
|
gptkbp:numberOfConnectedComponents
|
2
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite
|
|
gptkbp:realPointsOf
|
GL_n
|
|
gptkbp:relatedTo
|
gptkb:symmetry
change of basis
automorphism group of R^n
|
|
gptkbp:topology
|
real Lie group topology
|
|
gptkbp:bfsParent
|
gptkb:St_n(R)
gptkb:GL_n(Z)
|
|
gptkbp:bfsLayer
|
7
|