Let $U \subset \mathbb{R}^n$ be open, let $f: U \to \mathbb{R}$ belong to $C^2(U)$, and let $x_0 \in U$. For each $x \in U$, let $Hf_x \in \mathbb{R}^{n \times n}$ denote the Hessian matrix of $f$ at $x$, with entries $(Hf_x)_{ij} = \partial_{x_i}\partial_{x_j}f(x)$.