Bilinear form/Symmetric/Definition

Let ${\displaystyle {}K}$ be a field, let ${\displaystyle {}V}$ be a ${\displaystyle {}K}$-vector space, and let ${\displaystyle {}\left\langle -,-\right\rangle }$ denote a bilinear form on ${\displaystyle {}V}$. The bilinear form is called symmetric, if

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

holds for all ${\displaystyle {}v,w\in V}$.