  For partially ordered sets $X$ we consider the square matrices $M^{X}$ with
rows and columns indexed by linear extensions of the partial order on $X$. Each
entry $\left( M^{X}\right)_{PQ}$ is a formal variable defined by a pedestal of
the linear order $Q$ with respect to linear order $P$. We show that all the
eigenvalues of any such matrix $M^{X}$ are $\mathbb{Z}$-linear combinations of
those variables.
