Matrix norm using sup norm

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Hi all,

I want to make some modifications in the matrix norm. I'm trying to find $\sup_{x\neq0} \frac{\lVert Ax \rVert}{\lVert x \rVert}$

with different norms defined over denominator and numerator. As all other norms are defined I'm just curious about the source codes of them and also interested to see how to get the supremum or infimum in sage where $x\in V$ where V is a vector space.