On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

Christopher J. Hillar, Charles R. Johnson

It is shown that the polynomial \[p(t) = \text{Tr}[(A+tB)^m]\] has positive coefficients when $m=6$ and $A$ and $B$ are any two 3-by-3 complex Hermitian positive definite matrice…