Symmetric bilinear form/Degeneracy space/Definition

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

${\displaystyle {\left\{v\in V\mid \left\langle v,u\right\rangle =0{\text{ for all }}u\in V\right\}}}$

is called the degeneracy space of the bilinear form.