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\newcommand{\ie}{{\it i.e.}}  \subsubsection*{Complex gradient}  Suppose $f: \complex^n \to \reals$ is a real-valued function defined for $x \in \complex^n$. The gradient $\nabla f(x)$ is an $n \times 1$ matrix,\ie, it is  a \textit{row} vector. vector,  and defined as \begin{equation} \nabla f(x) = Df(x)^T = \left[   \begin{array}{c} \frac{\partial f}{\partial x_1}(x) \\ \vdots \\ \frac{\partial f}{\partial x_n}(x) \end{array} \right]. \nonumber  \end{equation}