Linear subspace in dual space/Orthogonal space/Definition

Orthogonal space (linear subspace in dual space)

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

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

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