# $\color{ffffff}\colorbox{#808080}{- Matrices Hessianas -}$ --- ⚪ #Definición > [!CDDefinición] $~$ Matriz Hessiana de una Función de $\mathbb{R}^{n}$ en $\mathbb{R}$ > > Sean $U\subseteq \mathbb{R}^{n}$ [[Conjunto Abierto y Conjunto Cerrado|abierto]], $f: U\to \mathbb{R}$ una [[Función|función]] de [[diferenciable|clase]] $C^{2}$ y $x_{0}\in U$. > > Definimos y denotamos la **matriz Hessiana** de $f$ en $x_{0}$ como: > > $H_{f}(x_{0})=\begin{pmatrix}\displaystyle{\frac{\partial^{2}f }{\partial x_{1}^{2}}}(x_{0}) & \displaystyle{\frac{\partial^{2} f}{\partial x_{1}\partial x_{2}}}(x_{0})&\cdots&\displaystyle{\frac{\partial^{2} f}{\partial x_{1}\partial x_{n}}}(x_{0})\\\displaystyle{\frac{\partial^{2}f }{\partial x_{2}x_{1}}}(x_{0}) & \displaystyle{\frac{\partial^{2} f}{\partial x_{2}^{2}}}(x_{0})&\cdots&\displaystyle{\frac{\partial^{2} f}{\partial x_{2}\partial x_{n}}}(x_{0})\\\vdots&\vdots&\ddots&\vdots\\\displaystyle{\frac{\partial^{2}f }{\partial x_{n}x_{1}}}(x_{0}) & \displaystyle{\frac{\partial^{2} f}{\partial x_{n}\partial x_{2}}}(x_{0})&\cdots&\displaystyle{\frac{\partial^{2} f}{\partial x_{n}^{2}}(x_{0})}\end{pmatrix}\in \mathcal{M}_{n}(\mathbb{R})$ > --- ### <font style="color:808080"> Links: </font> [[Matriz]] | [[diferenciable|clase]] | [[Conjunto Abierto y Conjunto Cerrado|abierto]] | [[derivadas cruzadas]] | [[derivadas parciales]] ---