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It goes both ways. Mathematicians will take a moment denigrate Geometric Algebra as "linear algebra with a uselessly nonstandard notation", ignoring that we sh
by gowld 2y ago
It goes both ways.
Mathematicians will take a moment denigrate Geometric Algebra as "linear algebra with a uselessly nonstandard notation", ignoring that we should prefer a less awkward way of structuring linear algebra than "pseudoscalars" and "pseudovectors".
- aleph_minus_one 2y ago> Mathematicians will take a moment denigrate Geometric Algebra as "linear algebra with a uselessly nonstandard notation", ignoring that we should prefer a less awkward way of structuring linear algebra than "pseudoscalars" and "pseudovectors". I have never heard a mathematician using the terms "pseudoscalar" and "pseudovector". These rather seem to be common terms among physicists.
- prof-dr-ir 2y ago> "linear algebra with a uselessly nonstandard notation" Let me chime in that as a physicist (who does use the "pseudo" stuff occasionally) I very much share this opinion. The notation may be really cool and compact, but I just do not see the benefit - for example, d*F = j and dF = 0 is compact enough for me. It is all fine if people use this language to learn linear algebra or differential geometry. And maybe it has a use for numerics or computer science. But I am quite sure that the geometric algebra formalism will not be widely adopted in physics any time soon. Sorry.
- gugagore 2y agoWhat other way is there around avoiding polar vs axial vectors looking the same but behaving differently? Or normal vs tangent vectors transforming differently?
- ajkjk 2y agoThose concepts are from exterior algebra which GA is built on. You do not need GA (the geometric product, etc) for them.
- gugagore 2y agoThat'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.
- 2y ago