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Re: help stamp out cross products
From
: "John S. Denker" <
jsd@MONMOUTH.COM
>
Date
: Thu, 8 Aug 2002 12:10:52 -0400
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.
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