and}
\\\
z_{i,j} \, \prod_{i&#39;=1}^{i-1} \left( 1 - z_{i&#39;\!,\,j}^2 \right)^{1/2}
&amp; \mbox{ if } 1 &lt; i &lt; j.
\end{array}
\right.
\]</span></p>
<p>This does not require as much computation per matrix entry as it may appear;
calculating the rows in terms of earlier rows yields the more
manageable expression</p>
<p><span class="math display">\[
w_{i,j} =
\left\{
\begin{array}{cl}
0 &amp; \mbox{if } i &gt; j,
\\
1 &amp; \mbox{if } 1 = i = j,
\\
z_{i,j} &amp; \mbox{if } 1 = i &lt; j, \mbox{ and}
\\
