Thread: Basis ambiguity? View Single Post
 Emeritus Sci Advisor PF Gold P: 16,091 It is true that if the sequences vi' and wi' are each a basis, then every element in $V \otimes W$ can be written uniquely as $$\sum_i \sum_j c_{ij} (v_i' \otimes w_j')$$ 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.