Linear subspace/Orthogonal space in dual space/Definition

Orthogonal space

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

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

the orthogonal space of ${}U$.