prod_{n=1}^{m} z_{n,n}
\ = \
\prod_{n=1}^K \ \prod_{m=n}^K z_{n,n}
\ = \
2^{K} \ \prod_{k=1}^K z_{k,k}^{K - k + 1}.
\]</span></p>
<p>Finally, the full absolute Jacobian determinant of the inverse
of the covariance matrix transform from the unconstrained lower-triangular
<span class="math inline">\(y\)</span> to a symmetric, positive definite matrix <span class="math inline">\(x\)</span> is the product of the
Jacobian determinants of the exponentiation and product transforms,</p>
<p><span class="math display