Hessian

For a scalar valued function \(f\), the Hessian is the matrix of second partial derivatives of the function's result with respect to its arguments.
\[ \mathbf{H}(f) = \begin{pmatrix} \frac{\partial^2 f}{\partial x_0^2} & \frac{\partial^2 f}{\partial x_0 \partial x_1} & \dots & \frac{\partial^2 f}{\partial x_0 \partial x_n}\\ \frac{\partial^2 f}{\partial x_1 \partial x_0} & \frac{\partial^2 f}{\partial x_1^2} & \dots & \frac{\partial^2 f}{\partial x_1 \partial x_n}\\ \vdots & \vdots & \ddots & \vdots &\\ \frac{\partial^2 f}{\partial x_n \partial x_0} & \frac{\partial^2 f}{\partial x_n \partial x_1} & \dots & \frac{\partial^2 f}{\partial x_n^2} \end{pmatrix} \]