# symmetric matrix

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

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

1. 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 SymmetricMatrix 2013-03-22 12:00:58 2013-03-22 12:00:58 Daume (40) Daume (40) 13 Daume (40) Definition msc 15-00 symmetric SelfDual HessianMatrix SkewHermitianMatrix