|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
Euclidean 3-space
|
|
gptkbp:application
|
gptkb:geometry
computer graphics
crystallography
physics
robotics
|
|
gptkbp:centralTo
|
{I, -I}
|
|
gptkbp:compact
|
true
|
|
gptkbp:connectedComponent
|
gptkb:SO(3)
|
|
gptkbp:contains
|
special orthogonal group SO(3)
|
|
gptkbp:defines
|
group of 3x3 real orthogonal matrices
|
|
gptkbp:determinant
|
±1
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:field
|
real numbers
|
|
gptkbp:hasSubgroup
|
gptkb:symmetric_group_S_n
cyclic group C_n
dihedral group D_n
general linear group GL(3, R)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
orthogonal group O(3)
|
|
gptkbp:includes
|
reflections
rotations
|
|
gptkbp:isometryGroupOf
|
Euclidean 3-space (linear isometries)
sphere S^2
|
|
gptkbp:matrixCondition
|
A^T A = I
|
|
gptkbp:numberOfConnectedComponents
|
2
|
|
gptkbp:order
|
infinite
|
|
gptkbp:preserves
|
gptkb:Euclidean_inner_product
length
Angle
|
|
gptkbp:realLieAlgebra
|
so(3)
|
|
gptkbp:relatedTo
|
gptkb:orthogonal_group_O(n)
orthogonal group O(2)
special orthogonal group SO(3)
general linear group GL(3, R)
|
|
gptkbp:structure
|
non-abelian
|
|
gptkbp:bfsParent
|
gptkb:Euclidean_group_E(3)
gptkb:SO(3)
gptkb:rotation_group_SO(3)
|
|
gptkbp:bfsLayer
|
7
|