Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
R^n
|
| gptkbp:centralTo |
{I, -I} (for n even)
{I} (for n odd) |
| gptkbp:compact |
true
|
| gptkbp:connectedComponent |
gptkb:SO(n,_R)
|
| gptkbp:containsElement |
n x n orthogonal matrices
|
| gptkbp:definedIn |
real numbers
|
| gptkbp:determinantOfElements |
1 or -1
|
| gptkbp:dimensions |
n
|
| gptkbp:hasSubgroup |
gptkb:general_linear_group_GL(n,_R)
|
| gptkbp:hasTwoComponents |
true
|
| https://www.w3.org/2000/01/rdf-schema#label |
orthogonal group O(n, R)
|
| gptkbp:isNonAbelian |
true (for n > 2)
|
| gptkbp:isSimple |
false
|
| gptkbp:notation |
gptkb:O(n,_R)
O(n) |
| gptkbp:orderOfFiniteVersion |
2
|
| gptkbp:preserves |
gptkb:Euclidean_inner_product
|
| gptkbp:relatedTo |
orthogonal transformations
reflections rotations isometries of R^n fixing the origin |
| gptkbp:specialSubgroup |
special orthogonal group SO(n, R)
|
| gptkbp:usedIn |
gptkb:geometry
group theory physics quantum mechanics representation theory |
| gptkbp:bfsParent |
gptkb:special_orthogonal_group_SO(n)
|
| gptkbp:bfsLayer |
6
|