B2. Hessian Matrix

The Hessian matrix $\mathop{\nabla }\nolimits ^2 r(\vec{x})$ of a scalar function $r(\vec{x})$ ( $\vec{x} \in \mathbb{R}^{n}$) is defined by the n x n matrix built out of the second partial derivatives

$$\mathop{\nabla }\nolimits ^2 r(\vec{x}) = \left ( \beg... ...tial^2 r(\vec{x})}{\partial x_n^2} \\ \end{array} \right ) .$$ (B3)

The Hessian matrix of the scalar function $r(\vec{x})$ is the Jacobian matrix of the gradient $\mathop{\nabla }\nolimits r(\vec{x})$.