$$H(F)=\left[\begin{array}{cccc}\frac{{\partial }^{2.}F}{\partial x_{1.}^{2.}}& \frac{{\partial }^{2.}F}{\partial x_{1.}\partial x_{2.}}& \cdots & \frac{{\partial }^{2.}F}{\partial x_{1.}\partial x_N}\\ \frac{{\partial }^{2.}F}{\partial x_{2.}\partial x_{1.}}& \frac{{\partial }^{2.}F}{\partial x_{2.}^{2.}}& \cdots & \frac{{\partial }^{2.}F}{\partial x_{2.}\partial x_N}\\ ⋮& ⋮& \ddots & ⋮\\ \frac{{\partial }^{2.}F}{\partial x_N\partial x_{1.}}& \frac{{\partial }^{2.}F}{\partial x_N\partial x_{2.}}& \cdots & \frac{{\partial }^{2.}F}{\partial x_N^{2.}}\end{array}\right]$$