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)=0 }
When
V is (
isomorphic to)
Rn and we make the standard identification of
V and
V*, the annihilator is just the
perpendicular subspace.