4 ms·
I don't quite understand why the author opposes quaternions and geometric algebra: the geometric product is almost exactly the formula for multiplying pure imag
by chombier 8y ago
I don't quite understand why the author opposes quaternions and geometric algebra: the geometric product is almost exactly the formula for multiplying pure imaginary quaternions (up to the real part sign).
These are just two constructions of isomorphic Clifford algebras which really are the same thing.
- eigenspace 8y agoThat's not true. The quaternions are the even subalgebra of the 3D geometric algebra. They are not isomorphic. Quaternions are isomorphic to the set of scalars and bivectors in the 3D geometric algebra but the 3D GA also has vectors and a volume form. This is just like how the complex numbers are isomorphic to the even subalgebra of the 2D geometric algebra. The geometric algebra is richer, more powerful, more generalizable and more coherent than the quaternion algebra, all while being easier to understand because its so physical.
- chombier 8y agoI stand corrected, thanks a lot! It seems the article mostly deals with the scalar/bivector aspect of it though.