finite
matrix), then there is a unique lower-triangular matrix <span class="math inline">\(z = \mathrm{chol}(x)\)</span> with positive diagonal entries, called a Cholesky
factor, such that</p>
<p><span class="math display">\[
x = z \, z^{\top}.
\]</span></p>
<p>The off-diagonal entries of the Cholesky factor <span class="math inline">\(z\)</span> are unconstrained,
but the diagonal entries <span class="math inline">\(z_{k,k}\)</span> must be positive for <span class="math inline">\(1 \leq k \leq K\)</span>.