Exercises
[11K] Prerequisites:[11F].Let’s consider square matrices, i.e. \(n=m\). We know from [11F] that norms \(\| A\| _{p,q}\) are submultiplicative, that is \(\| A B\| _{p,q}≤ \| A\| _{p,q} \| A\| _{p,q} \).
Show that the Frobenious norm is also submultiplicative.
Note that for a submultiplicative norm we have that \(\| A^ k\| ≤ \| A\| ^ k\) for every natural \(k\).