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)=0 }

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

An*ni"hi*la`tor (#), n.

One who, or that which, annihilates; as, a fire annihilator.


© Webster 1913.

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