Definition:Euclidean Norm

Definition
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:
 * $\ds \norm {\mathbf v} = \paren {\sum_{k \mathop = 1}^n v_k^2}^{1/2}$

Also see

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

Generalizations

 * Definition:P-Norm