[elengyel]

My position is that the geometric product and antiproduct are good for one thing, performing transformations with sandwich products q ⟑ p ⟑ q̃ or q ⟇ p ⟇ q̰ and composing those transformations. Literally everything else (join, meet, contraction, expansion, projection, inner product, norm, ...) can and should be done in the exterior algebra without any geometric products.

[ajkjk]

agree but I am still trying to grok the divine truth as to why exactly that is. What's up with the sandwich products? Why do they work? I guess it is like a change-of-basis for a matrix (PAP^{-1)) but I still don't quite see why, and why it works as a change-of-basis on multivectors, not just vectors.