Definition
23
[110]If \(M_ 1\), \(M_ 2\) are vector spaces with norms \(\| \| _{M_ 1}\) and respectively \(\| \| _{M_ 2}\), then \(π\) is an isometry when
\begin{equation} β x,yβ M_ 1, \| x-y\| _{M_ 1}=\| π(x)-π(y)\| _{M_ 2} \label{eq:isometria_ su_ normati} \end{equation}
24
(rewriting the definition of distance using norms).