(n\)</span>-dimensional vector <span class="math inline">\(x \in \mathbb{R}^n\)</span> is said to be a unit vector
if it has unit Euclidean length, so that</p>
<p><span class="math display">\[
\Vert x \Vert
\ = \ \sqrt{x^{\top}\,x}
\ = \ \sqrt{x_1^2 + x_2^2 + \cdots + x_n^2}
\ = \ 1\ .
\]</span></p>
<div id="unit-vector-inverse-transform" class="section level3 unnumbered">
<h3>Unit vector inverse transform</h3>
<p>Stan divides an unconstrained vector <span class="math inline">\(y \in \mathbb{R}^{n}\)</span>