Definition:Euclidean Norm

Definition
Let $\mathbf{v} = \left( {v_1, v_2, \ldots, v_n} \right)$ be a vector in the Euclidean $n$-space $\R^n$. The Euclidean norm of $\mathbf{v}$ is defined as:


 * $\displaystyle \left\Vert {\mathbf{v}} \right\Vert = \left( {\sum_{k=1}^n v_k^2} \right)^{1/2}$

Remark
That the Euclidean norm is a norm is proved in Euclidean Metric is a Metric.