Math Help - Annihilator

1. Annihilator

If anyone could help with this..

In space $M_2(\mathbb{C})$ there is a set:

$L= \begin{Bmatrix} \begin{bmatrix} -1 & 0 \\ 0 & i \end{bmatrix} , \begin{bmatrix} 0 & i \\ 1 & 0 \end{bmatrix} \end{Bmatrix}$

Find a basis for the annihilator $L^0$ of $L$ and complete it to a basis for the dual space of $M_2(\mathbb{C})$

Thank you

2. Re: Annihilator

Start by writing the definition of the annihilator.