e canonical partial correlations
as</p>
<p><span class="math display">\[
\mbox{det} \, x = \prod_{i=1}^{K-1} \ \prod_{j=i+1}^K \ (1 - z_{i,j}^2)
 = \prod_{1 \leq i &lt; j \leq K} (1 - z_{i,j}^2),
\]</span></p>
</div>
<div id="absolute-jacobian-determinant-of-the-correlation-matrix-inverse-transform" class="section level3 unnumbered">
<h3>Absolute Jacobian determinant of the correlation matrix inverse transform</h3>
<p>From the inverse of equation 11 in <span class="citation">(Lewandowski, Kurowicka, and Joe