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I'm curious about your perspective on exterior algebra. So far I've mostly seen it as a special case of GA so my view is probably GA-tinted. I'm just curious ho
by aap_ 2y ago
I'm curious about your perspective on exterior algebra. So far I've mostly seen it as a special case of GA so my view is probably GA-tinted. I'm just curious how you even do any sort of transformations since the exterior product doesn't allow these sorts of things. It seems like it only gives you the "things" in your algebra with few ways to do anything with them. You seem to agree with the author of the article you linked to in that the most useful aspects of GA come from EA. I find this very hard to see, so maybe you can shed some light on it? E.g. how do you rotate a bivector in EA?
- howling 2y agoThere is no equivalent notion of rotor in EA. I would say its most important use is that you need it to define differential form in which we can define exterior derivative and integeration in arbitrary differentiable manifolds. It also enables to define determinant elegantly.
- howling 2y agoSorry I forgot to answer your question: To rotate a bivector of the form v ^ w, just do R v ^ R w where R is the rotation matrix. This is a linear map so you can extend the operation linearly to arbitrary bivector.