Linear subspace in dual space/Orthogonal space/Definition

Orthogonal space (linear subspace in dual space)

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

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

is called the orthogonal space of $F$.