Special Orthogonal Group SO(2)
GPTKB entity
Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:topology gptkb:Lie_group |
| gptkbp:actsOn |
Euclidean plane
|
| gptkbp:application |
computer graphics
physics robotics plane rotations |
| gptkbp:centralTo |
gptkb:SO(2)
|
| gptkbp:compact |
true
|
| gptkbp:connects |
true
|
| gptkbp:dimensions |
1
|
| gptkbp:elements_are |
2x2 real orthogonal matrices with determinant 1
|
| gptkbp:fundamentalGroup |
isomorphic to Z
|
| gptkbp:generation |
rotation by angle θ
|
| gptkbp:hasSubgroup |
Orthogonal Group O(2)
Special Orthogonal Group SO(n) |
| https://www.w3.org/2000/01/rdf-schema#label |
Special Orthogonal Group SO(2)
|
| gptkbp:identityElement |
2x2 identity matrix
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
circle group U(1)
|
| gptkbp:Lie_algebra |
so(2)
|
| gptkbp:Lie_algebra_dimension |
1
|
| gptkbp:operator |
matrix multiplication
|
| gptkbp:order |
infinite
|
| gptkbp:parameter |
angle θ in [0, 2π)
|
| gptkbp:represents |
rotation matrices
|
| gptkbp:bfsParent |
gptkb:Special_Linear_Group_of_2x2_Real_Matrices
|
| gptkbp:bfsLayer |
8
|