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