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That's fine. That's still a step beyond just "linear algebra".
by gugagore 2y ago
That's fine. That's still a step beyond just "linear algebra".
- ajkjk 2y agoOh yes, strongly agree. They should be taught in linear algebra really.
- gugagore 2y agoHappy to have agreement that this goes beyond "traditional linear algebra". But, pedagogical treatment is a separate question from what is linear algebra. Should these all be the same wikipedia page? - https://en.wikipedia.org/wiki/Exterior_algebra https://en.wikipedia.org/wiki/Exterior_algebra - https://en.wikipedia.org/wiki/Multilinear_algebra https://en.wikipedia.org/wiki/Multilinear_algebra - https://www.georgehart.com/research/multanal.html https://www.georgehart.com/research/multanal.html (okay, not mainstream enough to have a relevant page, but it is extremely relevant in any engineering practice of linear algebra)
- ajkjk 2y agoWell by "taught in linear algebra" I mean "taught to undergraduates in their first or second year". It is totally bizarre that people learn about determinants, matrix minors, curl, magnetic fields, angular momentum, etc... but not about wedge products, in which all of these things are much easier to understand.
- gugagore 2y agoTotally agree! And this is why I sympathize with GA fanatics. Although it might not really make sense to do the rebranding or be maximalist about the geometric product, I do think there is a shared goal of making these things easier to understand.
- ajkjk 2y agoYa, as I write in my article, I'm very on board with the "change the curriculum to make more sense" project. I just want to be talking about how to do it in a critical way, rather than just going with the GA way, which requires, in my opinion, a lot of justification that I haven't seen.