\subsection{Cambiamento di base}
\begin{tabular}{ll}
$\Base = \{(1,0), (1,1)\}$ & $\Base' = \{(2,1),(1,2)\}$ \\
$(1,0) = (2/3,-1/3)_{|\Base'}$ & $(1,1) = (1/3,1/3)_{|\Base'}$ \\
\end{tabular}
$M_{\Base\rightarrow \Base'} =
\begin{bmatrix}
2/3 & 1/3 \\
-1/3 & 1/3 \\
\end{bmatrix}$
$\left((2,2)_{|\Base}\right)_{|\Base'} = M_{\Base\rightarrow \Base'} \cdot (2,2)_{|\Base} = (2,0)_{|\Base'}$
$M_{\Base'\rightarrow \Base} = M_{\Base\rightarrow \Base'}^{-1} =
\begin{bmatrix}
1 & -1 \\
1 & 2 \\
\end{bmatrix}$
$\left((2,0)_{|\Base'}\right)_{|\Base} = M_{\Base'\rightarrow \Base} \cdot (2,0)_{|\Base} = (2,2)_{|\Base'}$
