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doc: definition of Magnitude depends on notation which hasn't been defined #434

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donhatch opened this issue Sep 23, 2024 · 0 comments
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donhatch commented Sep 23, 2024

I had trouble trying to understand the definition of Magnitude from the doc at
https://clifford.readthedocs.io/en/latest/tutorials/g3-algebra-of-space.html?highlight=magnitude#Magnitude .

It says: "Using the reversion and grade projection operators, we can define the magnitude of A: |A|^2 = <A ~A>"

But this apparently depends on the notation <...> which hasn't been defined, as far as I can see.
(The previous section "Grade Projection" defines <...>_n but not <...>)

Eventually, from reading other sources (namely the footnote on page 3 of the Acus/Dargys paper "INVERSE OF MULTIVECTOR: BEYOND P+Q=5 THRESHOLD" at https://arxiv.org/pdf/1712.05204 ),
I came to the conclusion that it means <A ~A>_0
(i.e. the fix is to simply add the subscript "0").

(A possible alternative would be to define <...> to mean <...>_0 in the previous section, but I don't think it's necessary to introduce such new notation.)

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