[cbd1984]

Take a look at geometric algebra.

http://www.geometricalgebra.net/

http://en.m.wikipedia.org/wiki/Geometric_algebra

[GFK_of_xmaspast]

That's not quite the same, but worth reading up on anyway.

[cbd1984]

The quaternions are a subalgebra of geometric algebra. It's not quite the same in that it's strictly more general and, therefore, more broadly applicable.