I'd like to recover a rotor in geometric algebra where I know which (multi)vectors transform to given rotated (multi)vectors. I've found many references for 3D/4D dimensions (something like $\sum e_if_i$), but I need a formula for any dimension. Is there an easy one?
Also more importantly, how do I prove that it works?
Because I actually need to rotate multivectors $A_i=ae_i+cf_i$ (or maybe grade-3 basis) to new ones of this form, so that I will need to derive/check that the formula also works for a multivector basis.