this is for holding javascript data
Namgyun Lee edited newcommand_reals_mathbb_R_newcommand__.tex
about 8 years ago
Commit id: b6a8cc2749dd9a8f7eff639f9bde77873a0b2d30
deletions | additions
diff --git a/newcommand_reals_mathbb_R_newcommand__.tex b/newcommand_reals_mathbb_R_newcommand__.tex
index e7f4cc5..4f5f324 100644
--- a/newcommand_reals_mathbb_R_newcommand__.tex
+++ b/newcommand_reals_mathbb_R_newcommand__.tex
...
\newcommand{\reals}{\mathbb{R}}
\newcommand{\complex}{\mathbb{C}}
\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 matrix, \ie, it is a \textit{row} 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}