ity</em>. In
particular, it does <em>not</em> usually hold for three floating point numbers
<span class="math inline">\(a, b, c\)</span> that <span class="math inline">\((a + b) + c = a + (b = c)\)</span>.</p>
<p>In statistical applications, problems often manifest in situations
where users expect the usual rules of real-valued arithmetic to hold.
Suppose we have a lower triangular matrix <span class="math inline">\(L\)</span> with strictly positive
diagonal, so that it is the Cholesky factor of a positive-