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Homesymmetric matrix
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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:

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

$\begin{pmatrix}a&b&c\\ b&d&e\\ c&e&f\end{pmatrix}$
Related:
SelfDual, HessianMatrix, SkewHermitianMatrix
Synonym:
symmetric
Type of Math Object:
Definition
Major Section:
Reference
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Recent Activity
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new correction: Error in proof of Proposition 2 by alex2907
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Jun 6
new question: difference of a function and a finite sum by pfb
new correction: Error in proof of Proposition 2 by alex2907
Jun 24
new question: A good question by Ron Castillo
Jun 23
new question: A trascendental number. by Ron Castillo
Jun 19
new question: Banach lattice valued Bochner integrals by math ias
Jun 13
new question: young tableau and young projectors by zmth
Jun 11
new question: binomial coefficients: is this a known relation? by pfb
Jun 6
new question: difference of a function and a finite sum by pfb