norm

A vector's length, $\lVert\mathbf v\rVert = \sqrt{\mathbf v\cdot\mathbf v}$ .

For $\mathbf v = (v_1,\dots,v_n)$ , the norm (or length, or magnitude) of $\mathbf v$ , written $\lVert\mathbf v\rVert$ , is $\lVert\mathbf v\rVert = \sqrt{\mathbf v\cdot\mathbf v} = \sqrt{v_1^2+\cdots+v_n^2}$ — the Pythagorean theorem applied repeatedly. It is never negative, and it is $0$ only for the zero vector. The distance between two points $P,Q$ is $\lVert P-Q\rVert$ .