Norm : The norm $\lVert v\rVert$ of a vector $v=\begin{pmatrix}v_1\\v_2\\ \vdots \\v_n\\\end{pmatrix}$ is given by $\lVert v\rVert=\sqrt{v\cdot v}$ $=\sqrt{v_1^2+v_2^2+\ldots+v_n^2}.$ The norm of a vector intuitively describes the length of that vector.