Geometric product
For vectors:
ab = a^b + inner(a,b)
Associative, linear, but neither symmetric nor anti-symmetric
ba = b^a+inner(b,a) = -a^b+inner(a,b)
Advantage:
inverse exists
b*inverse(b) = 1
inverse(b) = b / inner(b,b)
In particular,
(a*b)/b = a
