\begin{definition}[Definition:Linear Isometry]
Let $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ be normed vector spaces.
Let $T : X \to Y$ be a linear transformation.
We say that $T$ is a '''linear isometry''' {{iff}}:
:$\norm {T x}_Y = \norm x_X$
for each $x \in X$.
\end{definition}