Let $A$ be an $n \times n$ matrix. Let $v$ be a right eigenvector of $A$ corresponding to the eigenvalue $\lambda_1$, and let $w$ be a left eigenvector of $A$ (which is a right eigenvector of $A^T$) corresponding to the eigenvalue $\lambda_2$. If $\lambda_1 \neq \lambda_2$, what is the value of the inner product $w^T v$?