z_{i,j} \ w_{i-1,j} \left( 1 - z_{i-1,j}^2 \right)^{1/2}
&amp; \mbox{ if } 1 &lt; i \leq j.
\end{array}
\right.
\]</span></p>
<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 th