3 ms·
Despite the name the motivation for the geometric product is principally algebraic, ie. it's useful for doing algebraic manipulation. It does not, AFAIK, posses
by edflsafoiewq 7y ago
Despite the name the motivation for the geometric product is principally algebraic, ie. it's useful for doing algebraic manipulation. It does not, AFAIK, possess any geometric meaning outside of special cases.
(It's "geometric" in the sense it doesn't depend on a choice of basis I guess.)
- DreamScatter 7y agoActually, it has a lot to do with geometry, in fact all of geometric algebra can be constructed from the geometric product, which serves as a foundation for not just algebra but also geometry. It encodes various geometric properties.
- edflsafoiewq 7y agoYes, it "encodes" them and they can be "constructed" from it, but it does not have a direct geometric interpretation in the way, say, the cross product does.