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Jun21-07, 05:54 PM
Sci Advisor
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Hurkyl's Avatar
P: 16,091
It is true that if the sequences vi' and wi' are each a basis, then every element in [itex]V \otimes W[/itex] can be written uniquely as

[tex]\sum_i \sum_j c_{ij} (v_i' \otimes w_j')[/tex]

But in my previous post I was simply stating something weaker. I was not assuming that vi' and wi' were bases; just they were just sequences of basis vectors. In particular, some basis vectors may be repeated, and others might not appear at all.