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| ``Re: A (better?) definition''
by siegelp on 2005-07-13 23:34:49 |
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| | I think the best way to define the cross product is the one involving tensor products; it has all of the same advantages as yours as well as the additional advantage that it becomes easy to generalize further. It is not totally clear, for instance, how to construct orthogonal subspaces of arbitrary codimension using your definition; i.e. it seems as though there should be a construction which specializes to the cross product in the case of codimension 1, but it is not so easy to articulate this construction without tensors. Still, any movement away from coordinates is a step in the right direction. |
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