Suppose we have two matrices, A and B, and
$\left\Vert A\right\Vert _{F}\geq\left\Vert B\right\Vert _{F}$
where $\left\Vert .\right\Vert _{F}$ denotes Frobenius norm. Does it imply
$\left\Vert A\right\Vert \geq\left\Vert B\right\Vert $
for any other norm $\left\Vert .\right\Vert $ ??
Thanks