a rotation matrix and <span class="arithmatex">\(T\)</span> is an upper-triangular scale/shear matrix.</p>
<p>(b) The first order Taylor series approximation has the form</p>
<div class="arithmatex">\[\begin{eqnarray}
    F^T(x, c, A) &amp;=&amp; F(x) + \sum_{\alpha \in\{c, \theta, T\}}\frac{\partial F}{\partial \alpha}(\alpha-\alpha_0)\non\\
    &amp;=&amp;F(x) + \nabla F(x)^T\sum_{\alpha\in \{c, \theta, T\}}\frac{\partial Z(x, x_0, c, A)}{\alpha}(\alpha-\alpha_0),\non
\end{eqnarray}\]</div>
<p>where <span