In the following paper https://arxiv.org/pdf/1611.00519.pdf, in lemma e.5, they state that if $Z\in \mathbb{R}^p$, $||\cdot||$ is the $p$-dimensional $l^2$ norm, and $\mathbb{S}^{p-1}$ is the unit sphere, then \begin{align} \Vert Z\Vert=\sup_{u\in \mathbb{S}^{p-1}}u^T z \end{align}
I don't understand why this holds.