nd{bmatrix} \succeq 0. ~
    \begin{bmatrix} y &amp; z \\ z &amp; x \end{bmatrix} \succeq 0.\end{split}\]</div>
<p>So <span class="math">\(k(3,1)=2\)</span>. An empirical study has shown that for
<span class="math">\(p=p_n/p_d&gt;1\)</span>, we have</p>
<div class="math">
\[k(p_n,p_d)\leq\log_2 p_n+\alpha(p_n)\]</div>
<p>where the <span class="math">\(\alpha(p_n)\)</span> term grows very slowly compared to the
<span class="math">\(\log_2\)</span> term. Indeed, for <span class="math">\(p_n\leq 4096\)</span>,