How to prove that any element of tensor product can be represented as $\sum \limits_{i=0}^{r}v_i \otimes w_i$, where vectors $v_1,\ldots,v_r \in V$ and vectors $w_1, \ldots w_r \in W$ are linear independent.
Prove that any element of vector space $V \otimes W$ can be represented as $\sum \limits_{i=0}^{r}v_i \otimes w_i$
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linear-algebra
vector-spaces
tensor-products