Let $A \in \mathbb{R}^{N \times N}$ be a D4571: Real matrix such that
| (i) | \begin{equation} A^T = A \end{equation} |
| (ii) | $\lambda, \mu \in \mathbb{C}$ are each a D1207: Complex number |
| (iii) | \begin{equation} \lambda \neq \mu \end{equation} |
| (iv) | $x, y \in \mathbb{R}^{N \times 1} \setminus \{ \boldsymbol{0} \}$ are each a D5200: Real column matrix |
| (v) | \begin{equation} A x = \lambda x \end{equation} |
| (vi) | \begin{equation} A y = \mu y \end{equation} |
Then
\begin{equation}
x^T y
= 0
\end{equation}