15-00-DiagonallyDominantMatrix.tex

\documentclass[12pt]{article}
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\pmcanonicalname{DiagonallyDominantMatrix}
\pmcreated{2013-03-22 13:47:46}
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\pmtitle{diagonally dominant matrix}
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\pmtype{Definition}
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\pmsynonym{diagonally dominant}{DiagonallyDominantMatrix}
\pmsynonym{strictly diagonally dominant}{DiagonallyDominantMatrix}
\pmdefines{strictly diagonally dominant matrix}

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\begin{document}
Let $A$ be a square matrix of order $n$ with entries $a_{ij}$ 
which are real or complex.  
Then $A$ is said to be \emph{diagonally dominant} if 
$$|a_{ii}| \geq \sum^n_{j=1, j\neq i} |a_{ij}|$$ 
for $i$ from $1$ to $n$.\\  
In addition $A$ is said to be \emph{strictly diagonally dominant} if 
$$|a_{ii}| > \sum^n_{j=1, j\neq i}|a_{ij}|$$
 for $i$ from $1$ to $n$.\\
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