|
gptkbp:instanceOf
|
gptkb:group_of_people
|
|
gptkbp:actsOn
|
gptkb:Vector
|
|
gptkbp:application
|
gptkb:geometry
gptkb:Lie_groups
crystallography
physics
quantum mechanics
representation theory
|
|
gptkbp:associativity
|
yes
|
|
gptkbp:closed
|
matrix multiplication
|
|
gptkbp:contains
|
orthogonal matrices
identity matrix
|
|
gptkbp:determinant
|
±1
|
|
gptkbp:dimensions
|
n(n-1)/2
|
|
gptkbp:field
|
gptkb:mathematics
|
|
gptkbp:finiteSubgroup
|
finite orthogonal group
|
|
gptkbp:generalizes
|
gptkb:Weyl_group
gptkb:rotation_group
gptkb:orthogonal_group_O(n,_F)
orthogonal group
|
|
gptkbp:hasSpecialCase
|
gptkb:orthogonal_group_O(n,_F)
orthogonal group
|
|
gptkbp:hasSubfield
|
group theory
linear algebra
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
orthogonal groups
|
|
gptkbp:identityElement
|
orthogonal group
identity matrix
|
|
gptkbp:infiniteFor
|
complex numbers
real numbers
|
|
gptkbp:inverseOperation
|
matrix inverse
|
|
gptkbp:isDefinedOver
|
gptkb:Field
|
|
gptkbp:isFinite
|
finite fields
|
|
gptkbp:isMatrixGroup
|
yes
|
|
gptkbp:matrixCondition
|
A^T A = I
|
|
gptkbp:namedFor
|
orthogonality
|
|
gptkbp:notation
|
O(n)
|
|
gptkbp:order
|
infinite (for real/complex fields)
|
|
gptkbp:preserves
|
inner product
quadratic form
|
|
gptkbp:relatedTo
|
gptkb:Pin_group
gptkb:Weyl_group
gptkb:Euclidean_group
gptkb:Lorentz_group
gptkb:Lie_group
gptkb:rotation_group
orthogonal group
|
|
gptkbp:bfsParent
|
gptkb:Bott_periodicity_theorem
|
|
gptkbp:bfsLayer
|
6
|