\displaystyle H(X)=
\left[\begin{array}{cccc}
\frac{\partial^2 f}{\partial x_1^2} & \frac{\partial^2 f}{\partial x_1\partial dx_2} & \ldots & \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} & \ldots & \frac{\partial^2 f}{\partial x_2\partial x_n}
\\ \vdots & \vdots & \ddots & \vdots
\\ \frac{\partial^2 f}{\partial x_n\partial dx_1} & \frac{\partial^2 f}{\partial x_n\partial x_2} & \ldots & \frac{\partial^2 f}{\partial x_n^2}
\end{array}\right]