K^n/Maximum norm/Example

In ${\displaystyle {}{\mathbb {K} }^{n}}$, taking

${\displaystyle {}\Vert {x}\Vert _{\rm {max}}:={\max {\left(\vert {x_{i}}\vert ,i=1,\ldots ,n\right)}}\,,}$

a norm is defined, which is called the maximum norm.