|
gptkbp:instanceOf
|
gptkb:mathematical_concept
Number system
|
|
gptkbp:algebraicStructure
|
Division algebra
Skew field
|
|
gptkbp:application
|
Rotation representation
Interpolation (slerp)
|
|
gptkbp:associative
|
true
|
|
gptkbp:basisFor
|
1
i
k
j
|
|
gptkbp:category
|
Hypercomplex numbers
|
|
gptkbp:commutative
|
false
|
|
gptkbp:component
|
Real numbers
|
|
gptkbp:conjugate
|
q* = a - bi - cj - dk
|
|
gptkbp:designer
|
q^{-1} = q*/|q|^2
|
|
gptkbp:dimensions
|
4
|
|
gptkbp:discoveredBy
|
gptkb:William_Rowan_Hamilton
|
|
gptkbp:discoveredIn
|
1843
|
|
gptkbp:fieldCharacteristic
|
0
|
|
gptkbp:generalizes
|
gptkb:Complex_numbers
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Quaternions
|
|
gptkbp:matrixRepresentation
|
4x4 real matrices
|
|
gptkbp:multiplicationRule
|
i^2 = j^2 = k^2 = ijk = -1
|
|
gptkbp:noncommutative
|
true
|
|
gptkbp:norm
|
Euclidean norm
|
|
gptkbp:relatedGroup
|
gptkb:SU(2)
gptkb:Spin(3)
|
|
gptkbp:relatedTo
|
gptkb:Clifford_algebras
gptkb:Dual_quaternions
gptkb:Octonions
|
|
gptkbp:symbol
|
gptkb:ℍ
|
|
gptkbp:usedFor
|
3D rotation calculations
Avoiding gimbal lock
|
|
gptkbp:usedIn
|
gptkb:robot
gptkb:signal_processing
gptkb:Animation
gptkb:Control_theory
gptkb:Quantum_mechanics
gptkb:Theoretical_physics
Computer vision
Navigation
3D computer graphics
Aerospace engineering
Virtual reality
Game development
Attitude control
|
|
gptkbp:bfsParent
|
gptkb:Euler_angles
|
|
gptkbp:bfsLayer
|
6
|