%---------------------------Jacobian---------------------------
\section{Jacobian}

This is the minimum determinant of the Jacobian matrix evaluated at each corner and the center of the element:
\[
q = \min\left\{\left\{\alpha_i\right\}_{i=0}^7, \frac{\alpha_8}{64} \right\}.
\]
This can also be interpreted as the minimum pointwise volume of local map
at the 8 corners and the center of the hexahedron.

\hexmetrictable{Jacobian}%
{$L^3$}%                                      Dimension
{$[0,DBL\_MAX]$}%                             Acceptable range
{$[0,DBL\_MAX]$}%                             Normal range
{$[-DBL\_MAX,DBL\_MAX]$}%                     Full range
{$1$}%                                        Cube
{\cite{knu:00}}%                              Citation
{v\_hex\_jacobian}%                           Verdict function name