Statements (32)
| Predicate | Object |
|---|---|
| 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 |
orthogonal group
|
| https://www.w3.org/2000/01/rdf-schema#label |
Special 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:rotation_group
orthogonal group |
| gptkbp:simple_for_n_>_2 |
yes
|
| gptkbp:bfsParent |
gptkb:SO(n)
|
| gptkbp:bfsLayer |
6
|