this is for holding javascript data
Namgyun Lee Deleted File
about 8 years ago
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\paragraph{Example 2.}
Given $x \in \complex^n$, What is $D\|x\|^2$? \\
%We have
%\begin{align*}
% |x| &= \sqrt{x^*x} = \sqrt{(a-jb)(a+jb)} = \sqrt{a^2 + b^2}. \\
%\end{align*}
%Then,
%\begin{eqnarray}
% D|x| &= \frac{d|x|}{da} + j\frac{d|x|}{db} \\
% &= \frac{2a}{2\sqrt{a^2 + b^2}} + j\frac{2b}{2\sqrt{a^2 + b^2}} \\
% &= \frac{a}{\sqrt{a^2 + b^2}} + j\frac{b}{\sqrt{a^2 + b^2}} \\
% &= \frac{x}{|x|}.
%\end{eqnarray}
