biVector forum

Exponential of 3D multivector

An arbitrary 3D multivector can be written as the superposition: M=Z+F, where Z=a+bi with a,b\in\mathbb R and i been the pseudo scalalar of (Cl_3). The remaining term F=v+iw, where v and w are vectors of Cl_3, has vector and bivector parts. Since Z\in Cen (Cl_3), the exponential of M becomes

To obtain a closed form of \exp(M), I would like to ask if there is a way to show that \exp(F)\stackrel{?}{=}\exp(v)\exp(iw)\ldots?. Thank you very much in advance.

Hi @peterlnx,

This is exactly the subject of Martin and my own latest writeup:

welcome to the forum!


I feel like I have a reference for the derivation of all these Cl(3) operations in my notes… ah yes, here: