April 17, 2010

LaTeX Example

funes latex

This document is generated as follows.

[ytyoun@Ordnung:~/doQment/]# xelatex test
[ytyoun@Ordnung:~/doQment/]# makeindex test
[ytyoun@Ordnung:~/doQment/]# makeindex test.nlo -s nomencl.ist -o test.nls
[ytyoun@Ordnung:~/doQment/]# xelatex test
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\documentclass[12pt]{article}
  
\usepackage{hyperref}
\usepackage[papersize={120mm, 160mm}, text={95mm, 130mm}]{geometry}
  
% fancy fonts
\usepackage{concrete}
  
% for fancy section font and color
\usepackage{color}
\definecolor{section_color}{rgb}{0.35,0.0,0}
\usepackage{sectsty}
\allsectionsfont{\color{section_color}\sffamily\selectfont}
  
% fancy math
\usepackage{amsmath,amssymb}
  
% mathematical shorthand
\newcommand{\Abf}{\ensuremath{\mathbf{A}}}
\newcommand{\ubf}{\ensuremath{\mathbf{u}}}
\newcommand{\vbf}{\ensuremath{\mathbf{v}}}
\newcommand{\xbf}{\ensuremath{\mathbf{x}}}
\newcommand{\Vcal}{\ensuremath{\mathcal{V}}}
\newcommand{\Rbb}{\ensuremath{\mathbb{R}}}
  
\newcommand{\norm}[1]{\ensuremath{\lVert{#1}\rVert}}
\newcommand{\proj}[2]{\ensuremath{\pi_{#1}(#2)}}
\newcommand{\trans}[1]{\ensuremath{{#1}^\top}}
\newcommand{\bkt}[1]{\ensuremath{\langle{#1}\rangle}}
  
% math operators
\DeclareMathOperator{\trace}{trace}
  
% index generation
\usepackage{makeidx}
\makeindex
  
% 'list of notations' generation
\usepackage[refpage]{nomencl}  % refer to the page where notation appears
\renewcommand{\nomname}{List of Notations}
\renewcommand*{\pagedeclaration}[1]{\unskip\dotfill\hyperpage{#1}}
\makenomenclature
  
\begin{document}
\paragraph{Matrix Norm}\index{Matrix Norm}
The squared \index{Matrix Norm!Frebenius norm}Frobenius norm of a matrix
$\Abf_{m\times n}$ is defined as
\nomenclature{$\norm{\Abf}_F$}{Frobenius norm of $\Abf$}
\begin{equation*}
  \norm{\Abf}_F^2 = \sum_{i=1}^m\sum_{j=1}^na_{ij}^2 =
  \trace(\trans\Abf\Abf).
\end{equation*}
  
The 2-norm\index{Matrix Norm!2-norm} of a matrix $\Abf_{m\times n}$ is
defined as\nomenclature{$\norm{\Abf}_2$}{2-norm of $\Abf$}
\begin{equation*}
\norm{\Abf}_2 = \max_{\norm{\xbf}_2=1}\norm{\Abf\xbf}_2\quad
\text{for $\xbf\in\Rbb^{n\times 1}$}
\end{equation*}
  
For a subspace $\Vcal\subseteq \Rbb^n$ and a vector $\ubf\in\Rbb^n$,
let $\proj{\Vcal}{\ubf}$
\nomenclature{$\proj{\Vcal}{\ubf}$}{Projection of $\ubf$ onto subspace $\Vcal$}
\index{Projection}
be the projection of $\ubf$ onto $\Vcal$.
If $\{\vbf_1,...,\vbf_k\}$ is a basis for $\Vcal$, then
\begin{equation*}
  \proj{\Vcal}{\ubf} = \sum_{i=1}^k \bkt{\vbf_i,\ubf}\vbf_i
\end{equation*}
  
\printnomenclature
\printindex
  
\end{document}
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