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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:
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Oct 21
new question: Prime numbers out of sequence by Rubens373
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new question: Lorenz system by David Bankom
Oct 19
new correction: examples and OEIS sequences by fizzie
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new correction: Define Galois correspondence by porton
Oct 7
new correction: Closure properties on languages: DCFL not closed under reversal by babou
new correction: DCFLs are not closed under reversal by petey
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new correction: Many corrections by Smarandache
Sep 28
new question: how to contest an entry? by zorba
new question: simple question by parag
new question: Prime numbers out of sequence by Rubens373
Oct 7
new question: Lorenz system by David Bankom
Oct 19
new correction: examples and OEIS sequences by fizzie
Oct 13
new correction: Define Galois correspondence by porton
Oct 7
new correction: Closure properties on languages: DCFL not closed under reversal by babou
new correction: DCFLs are not closed under reversal by petey
Oct 2
new correction: Many corrections by Smarandache
Sep 28
new question: how to contest an entry? by zorba
new question: simple question by parag