>
<p><span class="math display">\[
x_{i,j}
=
\left\{
\begin{array}{lll}
0 &amp; \mbox{ if } i &lt; j &amp; \mbox{ [above diagonal]}
\\
\sqrt{1 - \sum_{j&#39; &lt; j} x_{i,j&#39;}^2}
  &amp; \mbox{ if } i = j &amp; \mbox{ [on diagonal]}
\\
z_{i,j} \ \sqrt{1 - \sum_{j&#39; &lt; j} x_{i,j&#39;}^2}
  &amp; \mbox{ if } i &gt; j &amp; \mbox{ [below diagonal]}
\end{array}
\right.
\]</span></p>
<p>In the <span class="math inline">\(3 \times 3\)</span> case, this yields</p>
<p><span class="math display">\[
x =
\left