>\(x^\top x = 1\)</span> for any non-zero input vector
<span class="math inline">\(y\)</span>. Thus, there technically is no unique transformation from <span class="math inline">\(x\)</span> to
<span class="math inline">\(y\)</span>. To circumvent this issue, let <span class="math inline">\(r = \sqrt{y^\top y}\)</span> so that <span class="math inline">\(y = r x\)</span>. The transformation from <span class="math inline">\(\left(r, x_{-n}\right)\)</span> to <span class="math inline">\(y\)</span> is
well-def