\begin{definition}[Definition:Euclidean Norm]
Let $\mathbf v = \tuple {v_1, v_2, \ldots, v_n}$ be a vector in the Euclidean $n$-space $\R^n$.
The '''Euclidean norm''' of $\mathbf v$ is defined as:
:$\ds \norm {\mathbf v} = \paren {\sum_{k \mathop = 1}^n v_k^2}^{1/2}$
\end{definition}