|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
gptkb:Euclidean_space
|
|
gptkbp:application
|
gptkb:geometry
computer graphics
crystallography
physics
robotics
|
|
gptkbp:category
|
classical group
|
|
gptkbp:compact
|
yes
|
|
gptkbp:component
|
orthogonal group
orthogonal matrices with determinant -1
|
|
gptkbp:connects
|
no
|
|
gptkbp:contains
|
orthogonal group
|
|
gptkbp:containsElement
|
orthogonal group
|
|
gptkbp:defines
|
group of n×n orthogonal matrices with real entries
|
|
gptkbp:dimensions
|
n(n-1)/2
|
|
gptkbp:field
|
gptkb:mathematics
|
|
gptkbp:generalizes
|
gptkb:Weyl_group
gptkb:rotation_group
orthogonal group
|
|
gptkbp:hasSubfield
|
group theory
linear algebra
|
|
gptkbp:hasSubgroup
|
gptkb:group_of_people
dihedral group
orthogonal group
cyclic group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Orthogonal Group
|
|
gptkbp:identityElement
|
identity matrix
transpose matrix
|
|
gptkbp:Lie_group
|
yes
|
|
gptkbp:matrix_determinant
|
±1
|
|
gptkbp:notation
|
gptkb:O(n,_R)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:property
|
preserves angles
preserves inner product
preserves length
|
|
gptkbp:relatedTo
|
gptkb:general_linear_group
gptkb:Euclidean_group
gptkb:rotation_group
reflection
orthogonal group
orthogonal transformations
isometries
|
|
gptkbp:studiedBy
|
gptkb:Felix_Klein
gptkb:Hermann_Weyl
gptkb:Sophus_Lie
gptkb:Élie_Cartan
|
|
gptkbp:symbol
|
O(n)
|
|
gptkbp:bfsParent
|
gptkb:Orthogonal_Trading
|
|
gptkbp:bfsLayer
|
7
|