Motivation: Specifically understanding the "traditional" [[Vector Norms|vector norm]]. See also: [[Infinity-norm]] # 2-norm Also known as the Euclidean Norm. The 2-norm or $l_2$ norm denotes the Euclidean size of a vector. $||\vec{x}||_2 \equiv \sqrt{\sum_n^N |x_n|^2} $ So if we have a vector $\vec{v} = (-3,4)$, the 2-norm is found as follows: $||\vec{v}||_2 = \sqrt{(-3)^2 + (4)^2} = \sqrt{25} = 5$