$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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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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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.

Concepts

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Used In

Coming soon

Hypothesis

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FullPage
definition
concepts
used in
hypothesis
results
FullPage
definition
concepts
used in
hypothesis
results
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.

Concepts

Coming soon

Used In

Coming soon

Hypothesis

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Results

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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.

Concepts

Coming soon

Used In

Coming soon

Hypothesis

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Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results