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

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