  We study the computability of the operator norm of a matrix with respect to
norms induced by linear operators. Our findings reveal that this problem can be
solved exactly in polynomial time in certain situations, and we discuss how it
can be approximated for other cases. Along the way, we investigate the concept
of push-forward and pull-back of seminorms, which leads us to uncover novel
duality principles that come into play when optimizing over the unit ball of
norms.
