Definition – Norm\length of a vector.

Definition

Let $\mathbf{x} = (x_1, ..., x_m)$ be a vector in $\mathbb{R}^m$ . We define the norm (or length) of $x$ to be the positive square root of the dot product of $\mathbf{x}$ with itself,

$|\mathbf{x}| = \sqrt{\mathbf{x} \cdot{\mathbf{x}}} = \sqrt{x_1^2 + x_2^2 +, ..., + x_n^2}$