Linear subspace in dual space/Orthogonal space/Definition

Let ${\displaystyle {}V}$ be a ${\displaystyle {}K}$-vector space, and ${\displaystyle {}F\subseteq {V}^{*}}$ be a linear subspace of the dual space ${\displaystyle {}{V}^{*}}$ of ${\displaystyle {}V}$. Then

${\displaystyle {}F^{\perp }={\left\{v\in V\mid f(v)=0{\text{ for all }}f\in F\right\}}\subseteq V\,}$

is called the orthogonal space of ${\displaystyle {}F}$.