We consider in R 2 {\displaystyle {}\mathbb {R} ^{2}} the bases v = ( 3 − 7 ) , ( − 5 2 ) {\displaystyle {}{\mathfrak {v}}={\begin{pmatrix}3\\-7\end{pmatrix}},{\begin{pmatrix}-5\\2\end{pmatrix}}} and the standard basis e {\displaystyle {}{\mathfrak {e}}} , and we consider in C {\displaystyle {}\mathbb {C} } the real bases x = 8 − 2 i , 6 + 3 i {\displaystyle {}{\mathfrak {x}}=8-2{\mathrm {i} },6+3{\mathrm {i} }} and y = 1 , i {\displaystyle {}{\mathfrak {y}}=1,{\mathrm {i} }} . Determine the transformation matrix of the corresponding bases of the tensor product R 2 ⊗ R C {\displaystyle {}\mathbb {R} ^{2}\otimes _{\mathbb {R} }\mathbb {C} } .
