T-Annihilator of a Vector

Definition

Let $\alpha \in V$, then $M({\alpha }_{j}T)=\{f\in P(\mathbb{F})|f(T)\alpha =0\}$ is the $T$-annihilator of $\alpha$.

The Monic generators of $M({\alpha }_{j}T)$ is called the $T$-annihilator of $\alpha$

Properties

• This is a Polynomial Ideal.