% sample article for ELA (Electronic Journal of Linear Algebra)
% prepared by Daniel B Szyld, 3 Sept 1998
% this version uses the newest verison of latex Latex2e and the
% macros found in SIAM's web pasges.

%the siam latex style is used.
\documentstyle[10pt,twoside]{siamltex}

% text dimensions
\setlength{\textheight}{190mm}
\setlength{\textwidth}{130mm}
\topmargin = 15mm

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

%This environments are numbered within each section together with
%theorems, lemmas, etc.
%note: {\rm .... } should be used to have
%text in roman letters.
\newtheorem{remark}[theorem]{Remark}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{example}[theorem]{Example}


%the command \reals will give you the symbol for real numbers.
\newfont{\bb}{msbm10}
\def\Bbb#1{\mbox{\bb #1}}
\def\reals{ {\Bbb R}}
\def\complex{ {\Bbb C}}


\begin{document}

\bibliographystyle{plain}
\title{
Sample paper for ELA\thanks{Received by the editors on 18 January 1996.
Accepted for publication on 15 February 1997.
Handling Editor: John Matrix.}}
%Editors will write the exact dates.

\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{\mbox{Mathematics Department, Technion,
Haifa 32000, Israel
%mbox is used for better spacing, in some occasions.
(hershkow@math.technion.ac.il,} ~~~~~~ goldberg@math.technion.ac.il)
Example of the same affiliation for two people}
\and Moshe Goldberg\footnotemark[3]}
%If the same address is for the first and second person,
%\footnotemark[2] should be used.

%authors and runnnig title to go on top of the page
\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.
\end{abstract}

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

\section{Introduction} \label{intro-sec}
Each section start 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, consecutively throughout the paper,
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 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 text.
\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}
See, e.g., Varga \cite{varga-62}.
\end{proof}

\begin{remark}
{\rm
Remarks, as well as definitions, are in Roman letters.
Note that Lemma \ref{main-lem} and Theorem \ref{main-th} are in italics.
Note in the bibliography how a journal article like \cite{schneider-84}
is cited. Names of journals should be either completely spelled out, or
if abbreviated, the abbreviation should be the one used by {\em
Mathematical  Reviews}, available online at 
{\tt http://www.ams.org}. Consistency should be established for each paper: 
either all journal names are abbreviated, or none.
}
\end{remark}

Please note that for matrices, square brackets are used. Also note
that if the end of a proof  is a displayed formula, the end of the proof
mark should be in the line of the formula, as illustrated in the
following case.

\begin{lemma}
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,
$$
A =  \left[ \begin{array}{lr} a  & b \\ b &  c  \end{array}
\right].  ~~~~~~  \cvd
$$

In general, only formulas referenced in the text, such as 
(\ref{firstfor}) should be numbered, others can be included in the 
text or displayed. Similarly, one expects a reference in the text 
to every item listed in the bibliography.

\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.

\end{thebibliography}


\end{document}



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