Show that the eigenvectors belonging to distinct eigenvalues of a hermitian matrix are orthogonal to each other.

Let \( A \) be a Hermitian matrix, meaning that \( A = A^{\dagger} \), where \( A^{\dagger} \) is the conjugate transpose of \( A \). Suppose \( \mathbf{v}_1 \) and \( \mathbf{v}_2 \) are eigenvectors corresponding to distinct eigenvalues \( \lambda_1 \) and \( ____ ____ ____ __________ _____ ______ ______ ______ __________ ____ ___.
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