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Comment by ajkjk | Hacker News Reader

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ajkjk·

Oh yes, strongly agree. They should be taught in linear algebra really.

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Happy 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/Multilinear_algebra

- 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)

Well 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.

Totally 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.

Ya, 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.

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