Show that it is a sub-multiplicative norm, that is:
$$\forall ( u , v ) \in \mathcal { L } ( E ) ^ { 2 } , \quad \| u v \| \leqslant \| u \| \cdot \| v \| ,$$
and deduce a bound on $\left\| u ^ { k } \right\|$, for any natural number $k$, in terms of $\| u \|$ and the integer $k$.