symmetric matrixSymmetricMatrix2001-11-20 23:26:182006-09-20 13:40:57Definition\usepackage{amssymb}
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\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}