Grassmann Algebra

TheComplement.nb 34
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ei ���� ei � ���
More generally we have that for a basis m-vector, its complement in the n-plane is related to its
complement in the vector subspace by:
And for a general m-vector:
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ei � ��1� �� � ei
m
m
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Α � ��1� �� � Αm
m
The free complement of any exterior product involving the origin � is undefined.
The complement of an element bound through the origin
5.39
5.40
5.41
To express the complement of a bound element in the n-plane in terms of the complement in the
vector subspace we can use the complement axiom.
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More generally, we can show that for a general m-vector, the complement of the m-vector
bound through the origin in an n-plane is simply the complement of the m-vector in the vector
subspace of the n-plane.
2001 4 5
5.42