Definition:Direct Product Norm

Definition

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.

Also see

• Direct Product Norm is Norm