Clifford Algebra

An objects in Clifford Algebra can be thought of as a Complex Number only more so.

The basics
Two vectors in any number of dimensions can be multiplied according to this rule.

$$ab = (ab + ba)/2 + (ab - ba)/2 \,\!$$

The first term is the dot product of vector algebra, and has a scalar result.

$$a.b = (ab + ba)/2\,\!$$

The second term is termed the wedge product. The result of this is termed a bivector because it is the product of two vectors.

$$a\wedge b = (ab - ba)/2$$

Thus Clifford product can be expressed as

$$ab = a.b +  a\wedge b$$

2 dimensions
Assume 2 orthogonal basis vectors of unit size

more to come here - sorry incomplete

Resources

 * Clifford Algebra on WikiPedia
 * Clifford Algebra on WikiWikiWeb.
 * What is Clifford Algebra