this is for holding javascript data
Namgyun Lee edited newcommand_reals_mathbb_R_newcommand__.tex
about 8 years ago
Commit id: 262e48a337026e389e7eda56425303412a4da34c
deletions | additions
diff --git a/newcommand_reals_mathbb_R_newcommand__.tex b/newcommand_reals_mathbb_R_newcommand__.tex
index 973ff4c..6fe1574 100644
--- a/newcommand_reals_mathbb_R_newcommand__.tex
+++ b/newcommand_reals_mathbb_R_newcommand__.tex
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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, a matrix (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}