elements such that <span class="math inline">\(\Omega = L\,L^{\top}\)</span>. Because
the correlation matrix has a unit diagonal,</p>
<p><span class="math display">\[
\Omega_{k,k} = L_k\,L_k^{\top} = 1,
\]</span></p>
<p>each row vector <span class="math inline">\(L_k\)</span> of the Cholesky factor is of unit length. The
length and positivity constraint allow the diagonal elements of <span class="math inline">\(L\)</span> to
be calculated from the off-diagonal elements, so that a Cholesky
factor for a <span