general linear group GL(n, R)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:actsOn	R^n
gptkbp:centralTo	scalar matrices
gptkbp:component	gptkb:Z/2Z
gptkbp:containsElement	invertible n x n matrices
gptkbp:definedIn	real numbers
gptkbp:determinant	gptkb:special_linear_group_SL(n,_R) R\\{0}
gptkbp:dimensions	n^2
gptkbp:hasConnection	false
gptkbp:hasSubgroup	gptkb:special_linear_group_SL(n,_R) gptkb:general_linear_group_GL(n,_C)
https://www.w3.org/2000/01/rdf-schema#label	general linear group GL(n, R)
gptkbp:identityElement	identity matrix
gptkbp:isAlgebraicGroup	true
gptkbp:isDenseIn	gptkb:GL(n,_C)
gptkbp:isNonAbelian	true
gptkbp:isOpenSubsetOf	M(n, R)
gptkbp:isReductive	true
gptkbp:isSimple	false
gptkbp:Lie_algebra	gl(n, R)
gptkbp:LieAlgebraDimension	n^2
gptkbp:maximalCompactSubgroup	gptkb:orthogonal_group_O(n)
gptkbp:notation	gptkb:GL(n,_R)
gptkbp:numberOfConnectedComponents	2
gptkbp:order	infinite
gptkbp:relatedGroup	matrix multiplication
gptkbp:topology	real Lie group topology
gptkbp:bfsParent	gptkb:special_linear_group_SL(n,_R) gptkb:special_orthogonal_group_SO(n)
gptkbp:bfsLayer	6