Norms

Definition

The norm of a vector, denoted as $|\overrightarrow{\text{v}}|$ or $||\overrightarrow{\text{v}}||$, represents the vector’s magnitude (length).

• For a vector $\vec{v}\in {\mathbb{R}}^n$, its norm is calculated as $\Vert \vec{v}\Vert =\sqrt{v_1^2+v_2^2+\cdots +v_n^2}$ Norms provide a way to measure the size or length of vectors in vector spaces. $||\overrightarrow{v}||$ in Euclidean Space is also called $L_2$ norm.