Basis

The basis blades of a named algebra, ordered by grade then by generator — so comes back as .

WikipediaBasis (linear algebra)↗MathWorldVectorBasis↗WikidataQ189569↗Encyclopedia of Mathematicsbasis↗

Basis(algebra)the basis blades, as a list

Domain: Hypercomplex algebra

Details

• An algebra is an ordered list of generators; the families already carry the squares and the commutation rules
• Constructors: `CliffordAlgebra(p, q)`, `MulticomplexAlgebra(n)`, `SplitAlgebra(n)`, `DualAlgebra(n)`, `GrassmannAlgebra(n)`
• Named: Quaternions (also ), `BicomplexNumbers`, `TricomplexNumbers`, `SplitComplexNumbers`, `DualNumbers`
• No element constructor is needed — `Dot` threads a tuple of scalars over the basis

Examples

See also: Quaternions, AlgebraDimension, AlgebraSignature