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\[
\sum_{i=1}^{m}(\vec{v_{i}}) \bigotimes \sum_{j=1}^{n}(\vec{w_{j}}) =
(\vec{v}_{1}+\vec{v}_{2}+...+\vec{v}_{m}) \bigotimes (\vec{v}_{1}+\vec{v}_{2}+...+\vec{v}_{m}) =
(\vec{v}_{1} \bigotimes \vec{w}_{1})+ (\vec{v}_{1} \bigotimes \vec{w}_{2})+...+(\vec{v}_{1} \bigotimes \vec{w}_{n})
(\vec{v}_{2} \bigotimes \vec{w}_{1})+ (\vec{v}_{2} \bigotimes \vec{w}_{2})+...+(\vec{v}_{2} \bigotimes \vec{w}_{n}) +
...
+ (\vec{v}_{n} \bigotimes \vec{w}_{1})+ (\vec{v}_{n} \bigotimes \vec{w}_{2})+...+(\vec{v}_{n} \bigotimes \vec{w}_{n}) =
\sum_{i,j}^{n,m}(\vec{v_{i}} \bigotimes \vec{w_{j}}).
\]