Quaternions

, the quaternions — which IS : two anticommuting generators squaring to , with as the third unit.

WikipediaQuaternion↗MathWorldQuaternion↗WikidataQ173853↗Encyclopedia of MathematicsQuaternion↗nLabquaternion↗Britannicatopic/quaternion↗

Quaternions

\mathbb{H}the same algebra, written as a set

Domain: Hypercomplex algebra

Details

• , , , and
• Multiplication is NOT commutative: juxtaposition keeps the order, but an explicit does not -- use NonCommutativeMultiply (or ) there
• Usable as a set: is true, is false
• The other named algebras are `BicomplexNumbers`, `TricomplexNumbers`, `SplitComplexNumbers` and `DualNumbers`

Examples

See also: Basis, NonCommutativeMultiply, AlgebraSignature