Numerical Calculations in Clifford Algebra

6Vectors and Geometry

6.1 Theory

Vectors are represented in Clifford algebra by identifying the orthogonal unit vectors with particular Clifford units:

(6.1)

in a context, where the signature is either all or all . Vectors in three dimensions form a particular subset of three‐dimensional Clifford numbers. Although three‐dimensional Clifford numbers have four grades and eight components, vectors retain only one of the grades (grade 1) and three of the components. Vectors in dimensions higher than three require Clifford numbers of the corresponding dimension.

Table 6.1 lists the operations provided within the Clifford numerical suite for vectors of either signature. All multiplications are central (Clifford). Vectors , , and have real coefficients and unit length, and the symbol stands ...