|
gptkbp:instanceOf
|
gptkb:algebra
gptkb:group_of_people
|
|
gptkbp:actsOn
|
Euclidean space R^3
|
|
gptkbp:associativityProperty
|
true
|
|
gptkbp:category
|
gptkb:geometry
gptkb:mathematics
group theory
|
|
gptkbp:closed
|
composition of transformations
|
|
gptkbp:contains
|
reflections
translations
rotations
|
|
gptkbp:containsElement
|
isometries of R^3
|
|
gptkbp:dimensions
|
6
|
|
gptkbp:fieldOfStudy
|
gptkb:geometry
group theory
physics
|
|
gptkbp:hasInverseElement
|
true
|
|
gptkbp:hasNormalSubgroup
|
translations
|
|
gptkbp:hasSubgroup
|
gptkb:affine_group
gptkb:orthogonal_group_O(3)
special orthogonal group SO(3)
general linear group GL(4, R)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Euclidean group E(3)
|
|
gptkbp:identityElement
|
identity transformation
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isometryGroupOf
|
Euclidean space R^3
|
|
gptkbp:isomorphicTo
|
semidirect product of O(3) and R^3
|
|
gptkbp:isQuotientOf
|
O(3)
|
|
gptkbp:Lie_algebra
|
e(3)
|
|
gptkbp:namedAfter
|
gptkb:Euclid
|
|
gptkbp:notation
|
E(3)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:preserves
|
Euclidean distance
angles
|
|
gptkbp:usedIn
|
computer vision
crystallography
mechanics
robotics
rigid body motion
|
|
gptkbp:bfsParent
|
gptkb:3-dimensional_Euclidean_space
|
|
gptkbp:bfsLayer
|
6
|