Ononot — Let A be an n \times n matrix. Let v be a right eigenvector

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Eigenvalues & Eigenvectorsmedium

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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 $w^T v$ ?