Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
n-dimensional vector space over F
|
| gptkbp:centralTo |
{I, -I} (for n > 2, F not characteristic 2)
|
| gptkbp:consistsOf |
n x n orthogonal matrices over F
|
| gptkbp:definedIn |
field F
|
| gptkbp:determinant |
±1
|
| gptkbp:dimensions |
n(n-1)/2 (for F=R or C)
|
| gptkbp:hasApplication |
gptkb:geometry
computer science physics statistics |
| gptkbp:hasSpecialCase |
O(n, C) (complex orthogonal group)
O(n, R) (real orthogonal group) |
| gptkbp:hasSubgroup |
general linear group GL(n, F)
special orthogonal group SO(n, F) |
| gptkbp:heldBy |
gptkb:algebraic_geometry
group of isometries fixing the origin set of matrices A such that A^T A = I group of linear transformations preserving inner product |
| https://www.w3.org/2000/01/rdf-schema#label |
orthogonal group O(n, F)
|
| gptkbp:notation |
O(n, F)
|
| gptkbp:order |
infinite (if F is infinite)
|
| gptkbp:parameter |
F
n |
| gptkbp:preserves |
quadratic form
bilinear form |
| gptkbp:relatedTo |
gptkb:rotation_group
reflection |
| gptkbp:bfsParent |
gptkb:orthogonal_groups
|
| gptkbp:bfsLayer |
7
|