Let $A$ be a symmetric $n \times n$ matrix with eigenvalues $\lambda_1 \geq \cdots \geq \lambda_n$. Then \begin{align*} \lambda_1 = \max_{x \in \mathbb{R}^n \setminus \{0\}} \frac{\langle x, Ax \rangle}{\langle x, x \rangle}, \qquad \lambda_n = \min_{x \in \mathbb{R}^n \setminus \{0\}} \frac{\langle x, Ax \rangle}{\langle x, x \rangle}. \end{align*}