} \times \binom{K}{2}\)</span>, with indexes <span class="math inline">\((i,j)\)</span> for <span class="math inline">\((i &gt; j)\)</span>. The Jacobian
matrix is lower triangular, so that its determinant is the product of
its diagonal entries, of which there is one for each <span class="math inline">\((i,j)\)</span> pair,</p>
<p><span class="math display">\[
\left| \, \mbox{det} \, J \, \right|
  \ = \ \prod_{i &gt; j} \left| \frac{d}{dz_{i,j}} x_{i,j} \right|,
\]</span></p>
<p>where</p>
<p><span class="m