Let `V` be a vector space, let `V`^{*} be its dual vector space, and let `U` be a subspace (or just any subset) of `V`. The *annihilator* of `U` is

Ann `U` = { `f`∈`V`^{*} : ∀ `u`∈`U`.`f`(`u`)= }

When

`V` is (

isomorphic to)

**R**^{n} and we make the standard identification of

`V` and

`V`^{*}, the annihilator is just the

perpendicular subspace.