% Sample article for the Electronic Journal of Linear Algebra

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\documentclass[10pt,twoside]{siamltex}
\usepackage{amsfonts,epsfig}

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\setlength{\textwidth}{130mm}
\topmargin = 20mm

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% Box for end of proof outside environment
\def\cvd{~\vbox{\hrule\hbox{%
     \vrule height1.3ex\hskip0.8ex\vrule}\hrule } }

% Common extra environments
\newtheorem{remark}[theorem]{Remark}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{example}[theorem]{Example}

% Symbols for real and complex numbers
\newcommand{\reals}{\mathbb{R}}
\newcommand{\complex}{\mathbb{C}}

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\begin{document}

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% \input{elaheader-volx-xx.tex}
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\bibliographystyle{plain}
\title{
Sample paper for ELA\thanks{Received by the editors on Month x, 200x.
Accepted for publication on Month y, 200y   Handling Editor: .}}
% Leave blank; editors will write the exact dates above

\author{
Daniel B.\ Szyld\thanks{Department of Mathematics,
Temple University, Philadelphia, Pennsylvania 19122-6094, USA
(szyld@math.temple.edu). Supported by a generous grant from ILAS.}
% Remember to put \and between any two authors
\and
Danny Hershkowitz\thanks{Mathematics Department, Technion,
Haifa 32000, Israel (hershkow@math.technion.ac.il, \newline 
goldberg@math.technion.ac.il).}
\and 
Moshe Goldberg\footnotemark[3]}
% Note that \footnotemark[3]} is used for the third author
% because of the same affiliation for the second and third authors.
% If the same affiliation is to be used for the first and second authors,
% \footnotemark[2] should be used instead of \thanks{} for the second author.

% Authors and running title to go on top of each page
\pagestyle{myheadings}
\markboth{D.B.\ Szyld, D.\ Hershkowitz, and M.\ Goldberg}{Sample Paper}
\maketitle

\begin{abstract}
A good descriptive abstract is always very useful. The main results of
the paper are explained here of course, if possible. It should be written 
in the third person!
\end{abstract}

\begin{keywords}
Nonsingular matrices, Determinants, Spherical coordinates.
\end{keywords}
\begin{AMS}
15A15, 15F10. 
\end{AMS}

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\section{Introduction} \label{intro-sec}
Each section starts with a {\verb# \section{name} #} command.
The label is used to refer to it in other sections. Definitions, lemmas,
theorems, etc., are numbered consecutively within each section.
Formulas are numbered on the left as in the following equation:
\begin{equation} 
\label{firstfor}
Ax = b, 
\end{equation}
where $A$ is $n \times n$.

\begin{definition}
{\rm A square matrix $A$ is said to be {\em nonsingular} if its columns are 
linearly independent. }
\end{definition}

\begin{lemma} \label{main-lem}
If $A$ is $n \times n$ and nonsingular, the system {\rm (\ref{firstfor})} 
has a unique solution for any $b \in \reals^n$.
\end{lemma}

\begin{proof}
Consult any standard textbook (in linear algebra).
\end{proof}

\begin{corollary}
If $A$ is $n \times n$ and singular, the system {\rm (\ref{firstfor})} 
may have more than one solution.
\end{corollary}

\begin{theorem} \label{main-th}
Let $A$ be an $n \times n$ matrix. Then 
$\displaystyle{\lim_{k \rightarrow \infty}} A^k =O$ 
if and only if $\rho(A) <1$.
\end{theorem}

\begin{proof}
This is a well-known result; see e.g., Varga \cite[Some result]{varga-62}.
\end{proof}

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\section{Another section}
A few more items worth reading before you prepare an ELA article.
 
\begin{remark}
{\rm
\begin{itemize}
\item
Remark and Definition contents are in roman font, while
Lemma and Theorem statements are in italics.
\item
Note in the bibliography how a journal article like \cite{schneider-84}
is cited.  The journal name should be either completely spelled out or,
if abbreviated, the abbreviation should be the one used by 
{\em Mathematical Reviews} ({\tt http://www.ams.org}).
Consistency should be established in each paper: either all journal 
names are abbreviated, or none.
\item
Article \cite{ela-paper} is an example of a cited ELA paper.
The official abbreviation that can be used for ELA is
{\em Electron. J. Linear Algebra}.
\item
Use the macros {\verb# \reals #} to denote the real numbers $\reals$ and 
{\verb# \complex #} to denote the complex numbers $\complex$.
\item
Square brackets {\verb# \left[#} and {\verb# \right] #} are preferred for arrays.
\item
Only formulas referenced in the text, such as 
(\ref{firstfor}) or (\ref{below}) below, should be numbered; 
others can be included in the text or be displayed without numbers. 
Similarly, one expects a reference 
in the text to every item listed in the bibliography.
\item
When the end of a proof is a displayed formula, the end of the proof
mark should be in the line of the formula. Use the {\verb# \cvd #}
macro as illustrated in Lemma \ref{lem}.
\end{itemize}
}
\end{remark}

\begin{lemma}
\label{lem}
The off-diagonal entries of a $2 \times 2$ symmetric matrix 
are the same.
\end{lemma}

{\em Proof.}  
The proof follows from the structure of the matrix, as follows:
\begin{equation}
\label{below}
A =  \left[ \begin{array}{lr} a  & b \\ b &  c  \end{array}
\right]. ~~~~~~ \cvd
\end{equation}

% There are various ways to include postscript figures in a
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% Note that the epsfig package must be included in the preamble.

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% \epsfig{file=circle.eps,height=38mm,width=38mm,clip=}
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\bigskip
{\bf Acknowledgment.} We wish to thank everybody who has contributed
papers to the Electronic Journal of Linear Algebra.


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\begin{thebibliography}{1}
\bibitem{schneider-84}
Hans Schneider.
\newblock  Theorems on M-splittings of a singular M-matrix which
           depend on graph structure.
\newblock  {\em Linear Algebra and its Applications}, 58:407--424, 1984.

\bibitem{varga-62}
Richard S.~Varga.
\newblock  {\em Matrix Iterative Analysis}.
\newblock  Prentice-Hall, Englewood Cliffs, New Jersey, 1962.

\bibitem{ela-paper}
S.~Friedland and H.~Schneider. 
\newblock  Spectra of expansion graphs. 
\newblock  {\em Electronic Journal of Linear Algebra}, 6:2--10, 1999.

\end{thebibliography}
\end{document}


