 <span class="math inline">\(w\)</span> back to the array <span class="math inline">\(z\)</span> of
canonical partial correlations (CPCs) is simplified by the ordering of the elements in the
definition of <span class="math inline">\(w\)</span>, which when inverted yields</p>
<p><span class="math display">\[
z_{i,j} =
\left\{
\begin{array}{cl}
0 &amp; \mbox{if } i \leq j,
\\
w_{i,j} &amp; \mbox{if } 1 = i &lt; j, \mbox{ and}
\\
{w_{i,j}}
\
\prod_{i&#39;=1}^{i-1} \left( 1 - z_{i&#39;\!,j}^2 \right)^{-1/2}
&am