15-00-SymmetricMatrix.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{SymmetricMatrix}
\pmcreated{2013-03-22 12:00:58}
\pmmodified{2013-03-22 12:00:58}
\pmowner{Daume}{40}
\pmmodifier{Daume}{40}
\pmtitle{symmetric matrix}
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\pmprivacy{1}
\pmauthor{Daume}{40}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{15-00}
\pmsynonym{symmetric}{SymmetricMatrix}
\pmrelated{SelfDual}
\pmrelated{HessianMatrix}
\pmrelated{SkewHermitianMatrix}

\endmetadata

\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
%%%\usepackage{xypic}
\begin{document}
\PMlinkescapeword{properties}

\textbf{Definition:} \newline Let $A=(a_{ij})$ be a square matrix of
order $n$.  The matrix $A$ is \emph{symmetric} if $a_{ij} = a_{ji}$
for all $1 \leq i \leq n, 1 \leq j \leq n$.
\begin{center}$A =
\begin{pmatrix}
  a_{11} & \cdots & a_{1n} \\
  \vdots & \ddots & \vdots \\
  a_{n1} & \cdots & a_{nn}
\end{pmatrix}$
\end{center}

\textbf{Properties:}
\begin{enumerate}
  \item $A^t = A$ where $A^t$ is the matrix transpose
\end{enumerate}

\textbf{Examples:}
\begin{itemize}
  \item $\begin{pmatrix}
    a & b \\
    b & c 
  \end{pmatrix}$
  \item $\begin{pmatrix}
    a & b & c \\
    b & d & e \\
    c & e & f 
  \end{pmatrix}$
\end{itemize}
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\end{document}