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| Title of object: |
symmetric matrix |
| Canonical Name: |
SymmetricMatrix |
| Type: |
Definition |
| Created on: |
2001-11-20 23:26:18 |
| Modified on: |
2006-06-21 11:20:44 |
| Classification: |
msc:15-00 |
| Synonyms: |
symmetric matrix=symmetric |
Revision comment (for changes between this and next version):
| Changes for correction #9097 ('emphasis on defined terms and indicate what a_{ij} is'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic} |
Content:
\PMlinkescapeword{properties}
\textbf{Definition:} \newline Let $A$ be a square matrix of
order $n$. The matrix $A$ is 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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