Vector length
The non-negative scalar
\begin{equation*} \| \vec{v} \| = \left\| \begin{pmatrix} v_1 \\ \vdots \\ v_m \end{pmatrix} \right\| = \sqrt{{v_1}^2 + \cdots + {v_m}^2} = \sqrt{\sum_{i = 1}^{m} v_i^2}. \end{equation*}In terms of the dot product,
\begin{equation*} \| \vec{v} \| = \sqrt{\vec{v} \cdot \vec{v}}. \end{equation*}