|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:Euclidean_n-space
|
|
gptkbp:appearsIn
|
gptkb:geometry
physics
representation theory
linear algebra
|
|
gptkbp:centralTo
|
{I, -I} for n > 2
|
|
gptkbp:connectedComponent
|
gptkb:special_orthogonal_group_SO(n)
|
|
gptkbp:consistsOf
|
n x n orthogonal matrices
|
|
gptkbp:definedIn
|
real numbers
|
|
gptkbp:determinantOfElement
|
±1
|
|
gptkbp:dimensions
|
n(n-1)/2
|
|
gptkbp:elementsSatisfy
|
A^T A = I
|
|
gptkbp:fundamentalGroup
|
Z_2 for n > 2
|
|
gptkbp:hasSubgroup
|
gptkb:general_linear_group_GL(n,_R)
gptkb:special_orthogonal_group_SO(n)
|
|
gptkbp:heldBy
|
gptkb:Lie_group
closed subgroup of GL(n, R)
real algebraic group
real points of the orthogonal group over R
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
orthogonal group O(n)
|
|
gptkbp:Lie_algebra
|
so(n)
|
|
gptkbp:namedFor
|
orthogonality
|
|
gptkbp:notation
|
O(n)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:preserves
|
gptkb:Euclidean_inner_product
length
Angle
|
|
gptkbp:relatedTo
|
rotations and reflections
|
|
gptkbp:bfsParent
|
gptkb:compact_Lie_groups
gptkb:SO(n)
gptkb:Stiefel_manifold
gptkb:special_orthogonal_group_SO(n)
gptkb:linear_Lie_group
gptkb:unitary_group_U(n)
gptkb:inhomogeneous_orthogonal_group
|
|
gptkbp:bfsLayer
|
6
|