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Re: help stamp out cross products



Leigh Palmer wrote:

... pseudovectors ... (called "bivectors" in GA)

Not so fast. One of the great strengths of Geometric
Algebra is the unified view it provides of
-- D=2 flatland
-- D=3 space
-- D=1+3 spacetime

Bivectors are the pseudovectors in D=3 and not otherwise.
Let's not fall prey to D=3 provincialism.

In all generality, vectors have grade 1 while pseudovectors
have grade D-1.

Pascal's triangle for GA is

D=2 1 s 2 v 1 ps


D=3 1 s 3 v 3 bi-v 1 ps
(pv)

D=4 1 s 4 v 6 bi-v 4 tri-v 1 ps
(pv)

where v means vector, s means scalar, pv means pseudovector,
and ps means pseudoscalar.

Most of the things commonly called pseudovectors (in D=3)
are really bivectors (in D=2, D=3, and D=4, all the same).
Example: angular momentum.