## dual space problem

Hi all,

I am having trouble of with this problem. I think it isn't too difficult, but I am getting stuck. Any thoughts?

Let $v \in V$ be an eigenvector of T with corresponding eigenvalue $\lambda$. Let $w \in V^{*}$ be an eigenvector of the adjoint $T^{*}$ with eigenvalue $\lambda ^{*} \neq \lambda$.

Prove that $(v,w^{*}) = 0$