\begin{definition}[Definition:Isometric Isomorphism/Normed Vector Space]
Let $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ be normed vector spaces.
Let $T : X \to Y$ be a linear isometry.
We say that $T$ is an '''isometric isomorphism''' {{iff}} $T$ is bijective.
If an isometric isomorphism $T : X \to Y$ exists, we say that $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ are '''isometrically isomorphic'''.
\end{definition}