|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:abbreviation
|
gptkb:SO(n)
|
|
gptkbp:actsOn
|
gptkb:n-dimensional_Euclidean_space
|
|
gptkbp:application
|
gptkb:geometry
computer vision
mechanics
physics
robotics
|
|
gptkbp:center_for_n_even
|
object is {I}
|
|
gptkbp:center_for_n_odd
|
object is {I, -I}
|
|
gptkbp:compact
|
yes
|
|
gptkbp:connects
|
yes
|
|
gptkbp:consistsOf
|
orthogonal matrices with determinant 1
|
|
gptkbp:dimensions
|
n(n-1)/2
|
|
gptkbp:field
|
real numbers
|
|
gptkbp:generation
|
skew-symmetric matrices
|
|
gptkbp:hasSubgroup
|
gptkb:orthogonal_group
|
|
gptkbp:is_a_classical_group
|
yes
|
|
gptkbp:is_a_Lie_group
|
yes
|
|
gptkbp:is_a_real_algebraic_group
|
yes
|
|
gptkbp:is_a_real_Lie_group
|
yes
|
|
gptkbp:isMatrixGroup
|
yes
|
|
gptkbp:Lie_algebra
|
so(n)
|
|
gptkbp:notation
|
gptkb:SO(n,_R)
|
|
gptkbp:preserves
|
gptkb:Euclidean_inner_product
orientation
|
|
gptkbp:relatedTo
|
gptkb:orthogonal_group
gptkb:rotation_group
|
|
gptkbp:simple_for_n_>_2
|
yes
|
|
gptkbp:bfsParent
|
gptkb:Rotation_matrix
gptkb:SO(n)
|
|
gptkbp:bfsLayer
|
7
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Special orthogonal group
|