general linear group GL^+(n, R)
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
real n-dimensional vector space
|
| gptkbp:connectedComponentOf |
gptkb:general_linear_group_GL(n,_R)
|
| gptkbp:consistsOf |
n x n real matrices with positive determinant
|
| gptkbp:contains |
gptkb:special_linear_group_SL(n,_R)
|
| gptkbp:definedIn |
real numbers
|
| gptkbp:determinant |
positive real numbers
|
| gptkbp:dimensions |
n^2
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
gptkb:general_linear_group_GL(n,_R)
|
| https://www.w3.org/2000/01/rdf-schema#label |
general linear group GL^+(n, R)
|
| gptkbp:identityElement |
identity matrix
matrix inverse |
| gptkbp:isomorphicTo |
gptkb:SL(n,_R)_×_R^+
|
| gptkbp:notCompact |
true
|
| gptkbp:relatedGroup |
matrix multiplication
|
| gptkbp:usedIn |
differential geometry
physics representation theory linear algebra |
| gptkbp:bfsParent |
gptkb:connected_Lie_groups
|
| gptkbp:bfsLayer |
6
|