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"Rank" of a multivector

🔗Mike Battaglia <battaglia01@gmail.com>

5/4/2012 9:39:20 AM

Here's the definition of the "rank" of a multivector on Wikipedia:

http://en.wikipedia.org/wiki/Exterior_algebra#Rank_of_a_multivector

This deems a multivector's "rank" to be the minimal number of totally
decomposable multivectors needed to express the original multivector
as a linear combination. So by this definition, all valid wedgies are
"rank-1," meaning that they themselves are totally decomposable.
Multivals of rank > 1 are things which don't satisfy the Plucker
embedding conditions and as such can't be said to represent subspaces
of val space. (Sometimes I wonder what use they might have.)

So should I stop talking about the "rank" of a wedgie and instead
start talking about its "grade" or "dimension" something similar? It's
a shame that the word "rank" is used to mean something like
"dimensionality" in so many different areas of mathematics, but is
completely different here.

-Mike