Let $U\subseteq\mathbb{R}^n$, $f\in C^2(U, \mathbb{R})$, $\vec{a}\in U$. The Hessian matrix of $f$ at $\vec{a}$ is defined by $H=[H_{ij}]$, where $H_{ij}=\frac{\partial^2 f}{\partial x_i \partial x_j}(\vec{a})$. It is also denoted with $D^2f(\vec{a})$.
If $\text{det}(H)=0$, then $H$ is degenerate. Otherwise, if $\text{det}(H)\neq0$ it is nondegenerate.

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Let $U\subseteq\mathbb{R}^n$, $f\in C^2(U, \mathbb{R})$, $\vec{a}\in U$. The Hessian matrix of $f$ at $\vec{a}$ is defined by $H=[H_{ij}]$, where $H_{ij}=\frac{\partial^2 f}{\partial x_i \partial x_j}(\vec{a})$. It is also denoted with $D^2f(\vec{a})$.
If $\text{det}(H)=0$, then $H$ is degenerate. Otherwise, if $\text{det}(H)\neq0$ it is nondegenerate.

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