One approach to this is geometric algebra. I couldn't find a good reference that explains it intuitively, but there's this: http://en.wikipedia.org/wiki/Compari

One approach to this is geometric algebra. I couldn't find a good reference that explains it intuitively, but there's this: http://en.wikipedia.org/wiki/Comparison_of_vector_algebra_and_geometric_algebra#Matrix_Related http://en.wikipedia.org/wiki/Comparison_of_vector_algebra_an...