Geometry

   

Making Sense of Bivector Addition

Authors: James A. Smith

As a demonstration of the coherence of Geometric Algebra's (GA's) geometric and algebraic concepts of bivectors, we add three geometric bivectors according to the procedure described by Hestenes and Macdonald, then use bivector identities to determine, from the result, two bivectors whose outer product is equal to the initial sum. In this way, we show that the procedure that GA's inventors dened for adding geometric bivectors is precisely that which is needed to give results that coincide with those obtained by calculating outer products of vectors that are expressed in terms of a 3D basis. We explain that that accomplishment is no coincidence: it is a consequence of the attributes that GA's designers assigned (or didn't) to bivectors.

Comments: 18 Pages.

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Submission history

[v1] 2018-07-12 16:30:22
[v2] 2018-07-14 06:23:07

Unique-IP document downloads: 76 times

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