# Upper bound on the maximal eigenvalue of a matrix given the eigenvalues of Hadamard power of it

I have a matrix $$A$$ which has -1,1 outside the diagonal, and 0 on the diagonal. One can assume 1 on the diagonal(because all the eigenvalues can be related).

I am looking for an upper bound on the maximal eigenvalue of A in terms of the eigenvalues of $$A^{\circ 2}$$.

Hard to believe but maybe there is such a thing.

Thanks.