<p>Given the upper-triangular Cholesky factor <span class="math inline">\(w\)</span>, the final correlation matrix is</p>
<p><span class="math display">\[
x = w^{\top} w.
\]</span></p>
<p><span class="citation">Lewandowski, Kurowicka, and Joe (<a href="#ref-LewandowskiKurowickaJoe:2009">2009</a>)</span> show that the determinant of the correlation matrix can be defined in terms of the canonical partial correlations as</p>
<p><span class="math display">\[
\mbox{det} \, x = \prod_{i=1}^{K-1} \ \prod_{j=i+1}^K