general linear group GL(n,R)

URI: https://gptkb.org/entity/general_linear_group_GL(n,R)
GPTKB entity
Statements (36)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:topology
gptkb:Lie_group
gptkbp:actsOn R^n
gptkbp:centralTo scalar matrices
gptkbp:compact false
gptkbp:containsElement invertible n x n matrices
gptkbp:definedIn real numbers
gptkbp:determinant gptkb:SL(n,R)
det: GL(n,R) → R\\{0}
gptkbp:dimensions n^2
gptkbp:hasConnection false
gptkbp:hasMaximalSubgroup gptkb:orthogonal_group_O(n)
gptkbp:hasSubgroup gptkb:special_linear_group_SL(n,R)
gptkbp:hasTwoConnectedComponents true
https://www.w3.org/2000/01/rdf-schema#label general linear group GL(n,R)
gptkbp:identityElement identity matrix
gptkbp:isAlgebraicGroup true
gptkbp:isClassicalGroup true
gptkbp:isClosedIn M(n,R)
gptkbp:isDenseIn M(n,R)
gptkbp:isMatrixLieGroup true
gptkbp:isNonAbelian true
gptkbp:isOpenSubsetOf M(n,R)
gptkbp:isQuotientOf projective general linear group PGL(n,R)
gptkbp:isReductive true
gptkbp:isSimple false
gptkbp:isSolvable false
gptkbp:Lie_algebra gl(n,R)
gptkbp:notation gptkb:GL(n,R)
gptkb:GL_n(R)
gptkbp:order infinite
gptkbp:relatedGroup matrix multiplication
gptkbp:relatedTo automorphism group of R^n
gptkbp:bfsParent gptkb:special_linear_group_SL(n,R)
gptkbp:bfsLayer 7