Annihilator

The set of Linear Maps that will map all vectors in a vector space to 0

Definition

• Let $S$ be a Subset of Vector Space $V$ over Field $\mathbb{F}$
• The annihilator of $S$ is the set $S^o=\{T\in \mathcal{L}(V,\mathbb{F})|T(v)=0,\forall v\in S\}$

Theorems

• Annihilators are Subspaces
• Annihilators Defined by Perpendicular Sets