If you have used linear algebra (vectors and matrices) in visual computing before, then you know there are some difficulties that have to be overcome.

You end up jumping about between different systems, such as quaternions, Plucker coordinates and there is the need to convert things to points and back again not to mention dealing with special cases and odd transformations.

Doing this on paper is bad enough, it gets worse if you have to put it into code.

GA, which is still not that well known, provides a system that does away with a lot of  these problems.

By way of an introductory example, let's take a look at the vector cross product which should be familiar to everyone here.

Here is an obvious example of elements that do not "commute", axb is not equal to bxa.

The n with a little hat on (n hat) is the usual way to denote a vector of size 1, a unit vector.

The cross product itself is defined as

(Think I am going to wait for the math editor that is supposed to appear at next revision, I can just bodge it but it will look ugly and mar the explanation).