Induced matrix norm

Given a norm $\|\cdot\|_*$ of $\mathbb R^n$ we define a corresponding induced matrix norm according to the formula

$$ \|A\|_*=max_{x\in B_*}\|Ax\|_*, $$

being $B_*$ the unit ball of this norm:

$$ B_*=\{x\in \mathbb R^n:\|x\|_*=1\}. $$

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es


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