Inner product/K/Norm/Definition

Norm (associated to inner product)

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

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

the norm of ${}v$.