xt{tr}\left(\overset{\circ}{\mathbf{X}}^T\overset{\circ}{\mathbf{X}}\right)\)</span>. This phenomenon is clearly explained and also explored in the context of testing for sample independence by a <a href="https://projecteuclid.org/journals/annals-of-applied-statistics/volume-3/issue-3/Are-a-set-of-microarrays-independent-of-each-other/10.1214/09-AOAS236.full" class="external-link">2009 paper</a> of Efron.<br>
More broadly, a dataset <span class="math inline">\(\mathbf{X}\)</span> could arise from a multitud