 class="arithmatex">\(L=K-1\)</span> show that</p>
<div class="arithmatex">\[\begin{equation}
    \|z-\bar z_k\|^2 - \|z-\bar z_{k'}\|^2 = \|x-\bar x_k\|^2_W - \|x-\bar x_{k'}\|^2_W,\non
\end{equation}\]</div>
<p>where <span class="arithmatex">\(\|\cdot\|_W\)</span> denotes <em>Mahalanobis</em> distance with respect to the covariance <span class="arithmatex">\(W\)</span>.</p>
<p>(b) If <span class="arithmatex">\(L &lt; K-1\)</span>, show that the same expression on the left measures the difference in Mahala