Proof of the cases $p\le 7$ of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture

Daniel Haegele

It is shown that the polynomial $\lambda (t)=\mathrm{Tr}[(A+tB{)}^p]$ has nonnegative coefficients when $p\le 7$ and A and B are any two complex positive semidefinite $n\times n$ matric…