Linear subspace/Orthogonal space in dual space/Definition

For a linear subspace ${\displaystyle {}U\subseteq V}$ in a ${\displaystyle {}K}$-vector space, we call

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

the orthogonal space of ${\displaystyle {}U}$.