$\displaystyle A$ is a symmetric matrix containing only 0s and 1s; in particular all the diagonal entries are 0. $\displaystyle B$ is a symmetric positive definite matrix. I am interested in $\displaystyle T = \mathrm{trace}(AB)$. Is there a simple relation between $\displaystyle T$ and the eigenvalues of $\displaystyle A$ and $\displaystyle B$?