|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:3-dimensional_Euclidean_space
|
|
gptkbp:application
|
gptkb:geometry
computer vision
mechanics
physics
robotics
|
|
gptkbp:centralTo
|
trivial group
|
|
gptkbp:compact
|
true
|
|
gptkbp:containsElement
|
3x3 orthogonal matrices with determinant 1
|
|
gptkbp:determinantOfElements
|
1
|
|
gptkbp:dimensionOfLieAlgebra
|
3
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:fullName
|
gptkb:Special_Orthogonal_Group_in_3_dimensions
|
|
gptkbp:fundamentalGroup
|
gptkb:Z/2Z
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasInverseElements
|
true
|
|
gptkbp:hasSubgroup
|
O(3)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SO(3)
|
|
gptkbp:identityElement
|
true
|
|
gptkbp:isClosedUnderInversion
|
true
|
|
gptkbp:isClosedUnderMultiplication
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isomorphicTo
|
gptkb:projective_special_unitary_group_PSU(2)
|
|
gptkbp:isRealLieGroup
|
true
|
|
gptkbp:isSimple
|
true
|
|
gptkbp:isSmoothManifold
|
true
|
|
gptkbp:isTopologicalGroup
|
true
|
|
gptkbp:Lie_algebra
|
so(3)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:parameter
|
gptkb:Euler_angles
quaternions
axis-angle
|
|
gptkbp:relatedGroup
|
gptkb:rotation_group
|
|
gptkbp:relatedTo
|
gptkb:orthogonal_group_O(3)
gptkb:special_linear_group_SL(3)
gptkb:unitary_group_U(2)
quaternions
orthogonal matrices
rotation matrices
angular momentum
spin
rotational symmetry
rigid body motion
|
|
gptkbp:universalCover
|
gptkb:SU(2)
|
|
gptkbp:bfsParent
|
gptkb:SU(2)_symmetry
gptkb:旋转群
gptkb:特殊正交群
gptkb:SU(2)
gptkb:rotation_group
gptkb:3-sphere
|
|
gptkbp:bfsLayer
|
6
|