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

Also see

 * Euclidean Space is Normed Space, proving that the Euclidean norm is a norm.
 * Definition:Euclidean Metric

Generalizations

 * Definition:P-Norm