Cambridge University engineering lecturer Joan Lasenby discusses domains where geometric algebra methods offer clear advantages over standard vector calculus.
“Electromagnetism is also, I should have mentioned this, is a field whereby you really get huge simplification.”
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More from Joan Lasenby
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Lasenby: Geometric algebra unifies classical mechanics, linear algebra, and quantum physics
“So if you know this language, you can not only do rigid body dynamics in engineering, classical mechanics. You can do linear algebra without matrices and without tensors. And you can do complex things in quantum space-time physics with the same mathematical sy…”
Joan LasenbySep 17, 2018▶ 8:56Joan Lasenby on Applications of Geometric Algebra in Engineering · Y Combinator
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Lasenby: Rotation matrices are numerically inconvenient due to manifold constraints
“Rotation matrices are not numerically nice to deal with because you have to keep them on the manifold. You have to make sure if you change, if you update rotation matrices, you have to make sure it obeys the constraints.”
Joan LasenbySep 17, 2018▶ 13:34Joan Lasenby on Applications of Geometric Algebra in Engineering · Y Combinator
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Lasenby: Geometric algebra enables easy calculus on coordinate-free objects
“So I've said that I have these geometric objects, my rotations are objects, so I can write down coordinate free expressions. But not only can I write them down, I can differentiate with respect to them, easily. So, because I have this algebra of objects. I can…”
Joan LasenbySep 17, 2018▶ 21:36Joan Lasenby on Applications of Geometric Algebra in Engineering · Y Combinator
Insight
Lasenby: Geometric algebra requires more underlying compute but simplifies code
“Underlying, you've got an algebra of A much bigger algebra than three-dimensional space where I've got three vectors. So actually, computationally, there's more going on. There's more going on. Yeah, but at a higher level, you know, I can get code to do all th…”
Joan LasenbySep 17, 2018▶ 22:43Joan Lasenby on Applications of Geometric Algebra in Engineering · Y Combinator
Insight
Lasenby: Geometric algebra adds no new capabilities, only intuitive clarity
“Geometric algebra won't really give you anything that you can't do conventionally. What it might enable you to do is to see how, how to do that thing.”
Joan LasenbySep 17, 2018▶ 30:18Joan Lasenby on Applications of Geometric Algebra in Engineering · Y Combinator
Insight
Lasenby: Geometric algebra eliminates trial-and-error matrix hacks in computer vision
“If people have worked with computer vision, they will know that often things don't work. So instead of a rotation matrix R, they try R transpose. And instead of a translation vector T, they try R transpose T. And they mess around until it works because it's ki…”
Joan LasenbySep 17, 2018▶ 34:45Joan Lasenby on Applications of Geometric Algebra in Engineering · Y Combinator
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