EDB — 11K

Exercises

1. [11K] Prerequisites:[11F]↺↻.Let’s consider square matrices, i.e. $n=m$. We know from [11F]↺↻ that norms $\Vert A{\Vert }_{p,q}$ are submultiplicative, that is $\Vert AB{\Vert }_{p,q}\le \Vert A{\Vert }_{p,q}\Vert A{\Vert }_{p,q}$.

   Show that the Frobenious norm is also submultiplicative.

   Note that for a submultiplicative norm we have that $\Vert A^k\Vert \le \Vert A{\Vert }^k$ for every natural $k$.