Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:actsOn |
R^n
|
| gptkbp:compact |
true
|
| gptkbp:connectedComponent |
gptkb:SO(n,_R)
|
| gptkbp:contains |
gptkb:SO(n,_R)
|
| gptkbp:containsElement |
Orthogonal matrices
|
| gptkbp:describes |
The group of n×n real orthogonal matrices under matrix multiplication
|
| gptkbp:determinant |
±1
|
| gptkbp:dimensions |
n(n-1)/2
|
| gptkbp:field |
gptkb:Mathematics
gptkb:Group_theory gptkb:Linear_algebra |
| gptkbp:fullName |
gptkb:Orthogonal_group
|
| gptkbp:hasSubgroup |
gptkb:GL(n,_R)
|
| https://www.w3.org/2000/01/rdf-schema#label |
O(n, R)
|
| gptkbp:order |
Infinite
|
| gptkbp:preserves |
gptkb:Euclidean_inner_product
Angle Length |
| gptkbp:realForm |
O(n, C)
|
| gptkbp:type |
gptkb:group_of_people
|
| gptkbp:bfsParent |
gptkb:SO(n,_R)
|
| gptkbp:bfsLayer |
6
|