symmetric matrix

Definition:
Let $A=(a_{ij})$ be a square matrix of order $n$ . The matrix $A$ is symmetric if $a_{ij}=a_{ji}$ for all $1\leq i\leq n,1\leq j\leq n$ .

$A=\begin{pmatrix}a_{11}&\cdots&a_{1n}\\ \vdots&\ddots&\vdots\\ a_{n1}&\cdots&a_{nn}\end{pmatrix}$

Properties:

1.

$A^{t}=A$ where $A^{t}$ is the matrix transpose

Examples:

•

$\begin{pmatrix}a&b\\ b&c\end{pmatrix}$
•

$\begin{pmatrix}a&b&c\\ b&d&e\\ c&e&f\end{pmatrix}$

Title	symmetric matrix
Canonical name	SymmetricMatrix
Date of creation	2013-03-22 12:00:58
Last modified on	2013-03-22 12:00:58
Owner	Daume (40)
Last modified by	Daume (40)
Numerical id	13
Author	Daume (40)
Entry type	Definition
Classification	msc 15-00
Synonym	symmetric
Related topic	SelfDual
Related topic	HessianMatrix
Related topic	SkewHermitianMatrix