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 = { fV* : ∀ uU.f(u)= }

When V is (isomorphic to) Rn and we make the standard identification of V and V*, the annihilator is just the perpendicular subspace.