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Poor Foundations in Geometric Algebra
Eric Lengyel • August 23, 2024 You’ve got to get the fundamentals down, because otherwise the fancy stuff is not going to work. —Randy Pausch I have been involved in exterior algebra and geometric algebra research for about 15 years now.
The duct tape applied by the authors in this case was to use \(\mathbf I_n^{-1}\) instead of \(\mathbf I_n,\) but that causes problems if the pseudoscalar isn’t invertible (as in projective GA), so \(\mathbf{\widetilde I}_n\) or \(-\mathbf I_n\) arguably make better choices. It can't be that good because it would tell us there’s something fundamentally inefficient about linear algebra that we don’t understand.” If the conclusion was correct, then it would open new avenues of research into exactly why orthogonal matrix transformations are so bad. The authors have no idea what they’re talking about, they don’t understand what the Hodge dual does, and they’ve scribbled down the same kind of drivel that a student who skipped class would turn in for a homework assignment they didn’t know how to do.
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