an> defined on <span class="math inline">\(K \times K\)</span> covariance matrices is transformed to
the density <span class="math inline">\(p_Y(y)\)</span> over <span class="math inline">\(K + \binom{K}{2}\)</span> vectors <span class="math inline">\(y\)</span> by</p>
<p><span class="math display">\[
p_Y(y) = p_X(f^{-1}(y)) \ 2^K \ \prod_{k=1}^K z_{k,k}^{K-k+2}.
\]</span></p>
</div>
</div>
<div class="footnotes">
<hr />
<ol start="16">
<li id="fn16"><p>An alternative to the transform in this section, which