Inner product/K/Norm/Definition

Let ${\displaystyle {}V}$ denote a vector space over ${\displaystyle {}{\mathbb {K} }}$, endowed with an inner product ${\displaystyle {}\left\langle -,-\right\rangle }$. For a vector ${\displaystyle {}v\in V}$, we call the real number

${\displaystyle {}\Vert {v}\Vert ={\sqrt {\left\langle v,v\right\rangle }}\,}$

the norm of ${\displaystyle {}v}$.