Statements (48)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
number system |
| gptkbp:application |
gptkb:theoretical_physics
control theory robotics 3D computer graphics attitude control |
| gptkbp:basisFor |
1
i k j |
| gptkbp:category |
hypercomplex number
|
| gptkbp:component |
real number
|
| gptkbp:dimensions |
4
|
| gptkbp:discoveredBy |
gptkb:William_Rowan_Hamilton
|
| gptkbp:discoveredIn |
1843
|
| gptkbp:field |
gptkb:algebra
gptkb:mathematics |
| gptkbp:form |
a + bi + cj + dk
|
| gptkbp:generalizes |
complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hamilton quaternions
|
| gptkbp:multiplicationRule |
i^2 = j^2 = k^2 = ijk = -1
|
| gptkbp:property |
gptkb:division
associative skew field normed division algebra non-commutative basis is orthonormal with respect to the standard inner product associative under multiplication can be represented as 2x2 complex matrices can be used to avoid gimbal lock in 3D rotations contains subalgebra isomorphic to complex numbers contains subalgebra isomorphic to real numbers every nonzero element has a multiplicative inverse finite-dimensional algebra over the real numbers non-abelian group under multiplication not commutative under multiplication used in SLERP (spherical linear interpolation) |
| gptkbp:relatedGroup |
gptkb:quaternion_group
|
| gptkbp:relatedTo |
gptkb:octonions
gptkb:Clifford_algebras complex numbers real numbers |
| gptkbp:symbol |
gptkb:ℍ
|
| gptkbp:usedFor |
orientation in 3D space
rotation representation |
| gptkbp:bfsParent |
gptkb:Hurwitz_quaternion_order
|
| gptkbp:bfsLayer |
6
|