ScalingStacks

Definition 2.7. Let $(V,\lVert\mathord{\cdot}\rVert)$ be a finite-dimensional normed vector space. The dual norm of $\lVert\mathord{\cdot}\rVert^{\vee}$ on the dual vector space $V^{\vee}$ is defined by

$$\forall\ell\in V^{\vee},\ \lVert\ell\rVert^{\vee}:=\sup_{v\in V\setminus\{0\}}\frac{\lvert\ell(v)\rvert}{\lVert v\rVert}.$$