The geometric product is transform composition. It plays the same role as matrix multiplication: if a group is represented by a set of matrices or multivectors then the GP will be group composition.
For example Cl(4,2) can represent the spacetime conformal group and Cl(3,0,1) can represent the Euclidean group. If A and B are elements of those groups represented by multivectors then AB will be their composition.
That is an extremely fundamental operation. Almost as, if not more, fundamental than inner and wedge.
I mention this every time this article is posted on hacker news and nobody wants to talk about it :`(
For example Cl(4,2) can represent the spacetime conformal group and Cl(3,0,1) can represent the Euclidean group. If A and B are elements of those groups represented by multivectors then AB will be their composition.
That is an extremely fundamental operation. Almost as, if not more, fundamental than inner and wedge.
I mention this every time this article is posted on hacker news and nobody wants to talk about it :`(