Symmetric Matrix

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A Symmetric Matrix is a square matrix, [math]\displaystyle{ A=[a_{ij}]_{\substack{i=1\dots m\\j=1\dots m}} }[/math], that remains unchanged by the matrix transpose operation ([math]\displaystyle{ \mathbf{A}^{\mathrm{T}} = \mathbf{A} }[/math]), that is if [math]\displaystyle{ a_{ij} = \begin{cases} a_{ji} & \quad \text{if } i\#j\\ a_{ij} & \quad \text{if } i=j\\ \end{cases} }[/math]



References

2015