Vektorraum/Tensorprodukt/R^2 über sich/Rechnen/Beispiel

Im ${}\mathbb {R} ^{2}\otimes _{\mathbb {R} }\mathbb {R} ^{2}$ gilt

${}{\begin{aligned}{\begin{pmatrix}5\\-7\end{pmatrix}}\otimes {\begin{pmatrix}-3\\4\end{pmatrix}}&={\left(5e_{1}-7e_{2}\right)}\otimes {\left(-3e_{1}+4e_{2}\right)}\\&=-15e_{1}\otimes e_{1}+20e_{1}\otimes e_{2}+21e_{2}\otimes e_{1}-28e_{2}\otimes e_{2}.\end{aligned}}$