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gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:topology
gptkb:Lie_group
|
|
gptkbp:actsOn
|
projective space ℝP^n
ℝ^{n+1}
|
|
gptkbp:appearsIn
|
differential geometry
physics
representation theory
linear algebra
|
|
gptkbp:centralTo
|
scalar matrices with nonzero real entries
|
|
gptkbp:connectedComponentOfIdentity
|
matrices with positive determinant
|
|
gptkbp:connectedComponents
|
2
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|
gptkbp:containsElement
|
invertible (n+1)×(n+1) real matrices
|
|
gptkbp:determinantCondition
|
determinant ≠ 0
|
|
gptkbp:dimensions
|
(n+1)^2
|
|
gptkbp:field
|
ℝ
|
|
gptkbp:fullName
|
General Linear Group of degree n+1 over the real numbers
|
|
gptkbp:hasDeterminantMap
|
true
|
|
gptkbp:hasSubgroup
|
SL(n+1, ℝ)
|
|
gptkbp:homomorphismTo
|
GL(n+1, ℂ)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
GL(n+1, ℝ)
|
|
gptkbp:identityElement
|
matrix inverse
identity matrix of size (n+1)
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isQuotientOf
|
PGL(n+1, ℝ)
|
|
gptkbp:Lie_algebra
|
gl(n+1, ℝ)
|
|
gptkbp:noncompact
|
true
|
|
gptkbp:notSimple
|
true
|
|
gptkbp:realForm
|
GL(n+1, ℂ)
|
|
gptkbp:reductive
|
true
|
|
gptkbp:relatedGroup
|
matrix multiplication
|
|
gptkbp:bfsParent
|
gptkb:SO(n+1)
|
|
gptkbp:bfsLayer
|
7
|