\begin{definition}[Definition:Direct Product Norm]
Let $\struct {X, \norm {\, \cdot \,}}$ and $\struct {Y, \norm {\, \cdot \,}}$ be normed vector spaces.
Let $V = X \times Y$ be a direct product of vector spaces $X$ and $Y$ together with induced component-wise operations.
Let $\tuple {x, y} \in V$, $x \in X$ and $y \in Y$.
Then the '''direct product norm''' on $V$ is defined as:
:$\norm {\tuple {x, y} } := \map \max {\norm x, \norm y}$
where $\max$ denotes the max operation.
\end{definition}