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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,

\[\begin{equation*}
  \| \vec{v} \| = \sqrt{\vec{v} \cdot \vec{v}}.
\end{equation*}
\]

• Synonyms
• Intuit
• Implement