symmetric matrix

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A matrix that is equal to its transpose, i.e.,

A^{T} = A\,.

A real, symmetric matrix is also Hermitian.

Since the n\times n\, antisymmetric part of a matrix has \frac{n^2 - n}{2}\, independent components, it follows that a symmetric matrix has n^2 - \frac{n^2 - n}{2}= \frac{n^2 + n}{2} = \frac{n(n+1)}{2}\, independent components.

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