s="math inline">\(L\)</span> will be <span class="math inline">\(M \times M\)</span>. If
<span class="math inline">\(\Sigma\)</span> is only positive semi-definite, then <span class="math inline">\(L\)</span> will be <span class="math inline">\(M \times N\)</span>,
with <span class="math inline">\(N &lt; M\)</span>.</p>
<p>A matrix is a Cholesky factor for a covariance matrix if and only if
it is lower triangular, the diagonal entries are positive, and <span class="math inline">\(M \geq N\)</span>. A matrix