Norm

Definition

Let $\mathbf{v}=(v_1,v_2,\dots ,v_n)$ vector in $R^n$

Then the norm of $\mathbf{v}$ is defined as

$$||\mathbf{v}||=\sqrt{v_1^2+v_2^2+\cdots +v_n^2}$$

Remark

Norm of $\mathbf{v}$ is also often referred to as the length of $\mathbf{v}$ or the magnitude of $\mathbf{v}$.