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The Hadamard product or pairwise product of two matrices denoted hereby by "o"

C = A o B.

Let Lambda(A) be the set of all eigenvalues of matrix A.

I am aware of inequalities relating Lambda(A), Lambda(B), and Lambda(C).

It is possible that my question does not have any answer but I would just like to make sure that is there any closed form EQUALITY expressions relating Lambda(A), Lambda(B), and Lambda(C).

Thank you in advance.