f non-negative values summing to 1.</p>
<p>As these examples illustrate, the simplex always picks out a subspace
of <span class="math inline">\(K-1\)</span> dimensions from <span class="math inline">\(\mathbb{R}^K\)</span>. Therefore a point <span class="math inline">\(x\)</span> in the
<span class="math inline">\(K\)</span>-simplex is fully determined by its first <span class="math inline">\(K-1\)</span> elements <span class="math inline">\(x_1, x_2, \ldots, x_{K-1}\)</span>, with</p>
<p><span class="math 