For a matrix $A$, is there any relation between operator norm (https://en.wikipedia.org/wiki/Matrix_norm#Induced_norm) and infinity norm (defined as the maximum of the absolute value of all the entries) ?
[Math] inequality between operator norm and infinity norm
matricesnormed-spaces
Best Answer
The fact:
And it is easy to check the space of $n\times m$ matrices is a finite-dimensional vector space; also the operator norm and infinity norm are really norms.
So they are equivalent!
i.e.
$$||A||\le C_1||A||_{\infty}$$ and $$||A||_{\infty}\le C_2||A||$$
and that might be the relation you want.