|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:topology
gptkb:Lie_group
|
|
gptkbp:actsOn
|
R^2
projective line
|
|
gptkbp:centralTo
|
scalar multiples of identity matrix
|
|
gptkbp:component
|
gptkb:Z/2Z
|
|
gptkbp:connectedComponentOfIdentity
|
matrices with positive determinant
|
|
gptkbp:contains
|
gptkb:SL(2,_R)
|
|
gptkbp:containsElement
|
all 2x2 invertible real matrices
|
|
gptkbp:determinant
|
nonzero real number
|
|
gptkbp:dimensions
|
4
|
|
gptkbp:field
|
real numbers
|
|
gptkbp:fullName
|
general linear group of 2x2 invertible real matrices
|
|
gptkbp:hasConnection
|
false
|
|
gptkbp:hasSubgroup
|
gptkb:SO(2)
gptkb:SL(2,_R)
gptkb:O(2)
diagonal matrices
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(2, R)
|
|
gptkbp:identityElement
|
2x2 identity matrix
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isQuotientOf
|
gptkb:PGL(2,_R)
|
|
gptkbp:isReductive
|
true
|
|
gptkbp:isSimple
|
false
|
|
gptkbp:Lie_algebra
|
gl(2, R)
|
|
gptkbp:operator
|
matrix multiplication
|
|
gptkbp:order
|
infinite
|
|
gptkbp:representationTheory
|
well-studied
|
|
gptkbp:usedIn
|
control theory
differential geometry
physics
representation theory
linear algebra
|
|
gptkbp:bfsParent
|
gptkb:SO(2)
gptkb:SL(2,_R)
|
|
gptkbp:bfsLayer
|
7
|