|
gptkbp:instanceOf
|
gptkb:algebra
gptkb:division
non-commutative algebra
|
|
gptkbp:application
|
gptkb:navigation
gptkb:signal_processing
quantum mechanics
robotics
attitude control
quaternionic analysis
spatial rotations
|
|
gptkbp:automorphismGroup
|
gptkb:SO(3)
|
|
gptkbp:basisFor
|
1
i
k
j
|
|
gptkbp:category
|
hypercomplex numbers
|
|
gptkbp:centralTo
|
real numbers
|
|
gptkbp:conjugate
|
a - bi - cj - dk
|
|
gptkbp:designer
|
conjugate divided by norm squared
|
|
gptkbp:dimensions
|
4
|
|
gptkbp:discoveredBy
|
gptkb:William_Rowan_Hamilton
|
|
gptkbp:discoveredIn
|
1843
|
|
gptkbp:field
|
real numbers
|
|
gptkbp:form
|
a + bi + cj + dk
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Hamiltonian quaternions
|
|
gptkbp:multiplicationRule
|
i^2 = j^2 = k^2 = ijk = -1
ij = k
ik = -j
ji = -k
jk = i
ki = j
kj = -i
|
|
gptkbp:norm
|
sqrt(a^2 + b^2 + c^2 + d^2)
|
|
gptkbp:notation
|
H
|
|
gptkbp:property
|
associative
skew field
normed division algebra
non-commutative
|
|
gptkbp:relatedGroup
|
gptkb:quaternion_group
|
|
gptkbp:relatedTo
|
gptkb:octonions
gptkb:Clifford_algebras
complex numbers
|
|
gptkbp:symbol
|
gptkb:ℍ
|
|
gptkbp:usedIn
|
gptkb:theoretical_physics
computer graphics
control theory
3D rotations
|
|
gptkbp:bfsParent
|
gptkb:Lipschitz_quaternion
gptkb:icosian_ring
|
|
gptkbp:bfsLayer
|
7
|