General 1:1 transformations

When the transformation $ T({\bf x})$ is dimension-preserving and 1:1, there is no energy statistic or reference hypothesis needed since the J-function simplifies to the determinant of the Jacobian matrix of transformation $ T({\bf x})$, $ J({\bf x}; T) = \vert{\bf J}\vert,$ where

$\displaystyle {\bf J}_{i,j}= \frac{ \partial z_i}{\partial x_j}.$

Re-synthesis of $ {\bf x}$ is through the inversion of the 1:1 transform.


Baggenstoss 2017-05-19