# Norm In general a **norm** is simply defined as: $\Big( \sum_i^n \vert x_i \vert ^{\alpha} \Big) ^{\frac{1}{\alpha}}$ A familiar example is the **euclidean norm** (also called the **2-norm**, $l^2$, $L^2$) where $\alpha = 2$: $\Big( \sum_i^n \vert x_i \vert ^{2} \Big) ^{\frac{1}{2}} = \sqrt{\sum_i^n \vert x_i \vert ^{2}} = \sqrt{x_1^2 + \dots + x_n^2}$ Note that you will often see the euclidean norm written as $\Vert x \Vert _2$ or $\vert x \vert _2$. --- Date: 20230810 Links to: Tags: References: * [Norm (mathematics) - Wikipedia](https://en.wikipedia.org/wiki/Norm_(mathematics))