x, the absolute determinant of which is thus</p>
<p><span class="math display">\[
\prod_{k=1}^K  \frac{\partial}{\partial_{y_{k,k}}} \, \exp(y_{k,k})
\ = \
\prod_{k=1}^K \exp(y_{k,k})
\ = \
\prod_{k=1}^K z_{k,k}.
\]</span></p>
<p>The Jacobian matrix of the second transform from the Cholesky factor <span class="math inline">\(z\)</span> to
the covariance matrix <span class="math inline">\(x\)</span> is also triangular, with diagonal entries
corresponding to pairs <span class="math inline">\((m,n)\)</span> wi