Bilinear form/Corresponding quadratic form/Definition

For a bilinear form ${\displaystyle {}\left\langle -,-\right\rangle }$ on a ${\displaystyle {}K}$-vector space ${\displaystyle {}V}$, the mapping

${\displaystyle V\longrightarrow K,v\longmapsto \left\langle v,v\right\rangle }$

is called the corresponding quadratic form.