Symmetric matrices

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose... Wikipedia: Symmetric matrix

The sum of two symmetric matrices is symmetric.

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The product of two symmetric matrices is symmetric if and only if the matrices commute.

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For all n, A**n is symmetric if A is symmetric.

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If the inverse of a symmetric matrix exists, it is symmetric.

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The rank of a symmetric matrix is ​​equal to the number of non-zero eigenvalues.

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Let A be a square matrix: (A+AT) is symmetric, (A-AT) is a skew matrix

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Let A be a square matrix: A = (A+AT)/2 + (A-AT)/2

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The code

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