Numerical Calculations in Clifford Algebra

4Unary Operations

4.1 Theory

Five elementary unary operations, as listed in the middle section of Table 4.1, are provided within the Clifford numerical suite. The first four operations change the signs of some of the components, without ever affecting the units. The Hodge star operation changes some signs and always modifies units. It is not elementary in the sense that it is composed from simpler operations (reversion and central multiplication).

4.1.1 Negation

Negation of Clifford numbers involves changing the sign of every coefficient. Figure 4.1 depicts on the left‐hand side a numerical operation involving three primal units , , shown as boxes with two Clifford (central) multiplication operations and one negation operation. The central multiplication operations, for which there is no symbol, are located between the boxes.

The negation operation has the effect of multiplying the entity on its right‐hand side by the value . The result is shown on the right‐hand side of Figure 4.1. The three prime numbers ‘2 3 5’ joined by dots denotes the single Clifford number produced by multiplying ...