The [[Vector Norm|Norm]] of a [[Vector]] is a generalization of [[Vector Magnitude]]. [[Universal Quantifier|For any]] [[Real Numbers|Real]] or [[Complex Numbers|Complex]] [[Vector Space]] $V$, a [[Vector Norm|Norm]] is a [[Function|function]] notated as the following: $\huge || \cdot ||: V \to \R $ The [[Vector Norm|Norm]] is required to have the following properties; $\huge \begin{align} \forall \vec x,\vec y & \in V \\ || \vec x + \vec y || &\leq ||\vec x || + ||\vec y|| \\ || \vec x || &\geq 0 \\ ||\vec x || = 0 &\iff \vec x = \vec 0 \end{align} $