  In this paper, we consider the problem of reconstructing an $n \times n$ cell
matrix $D(\vec{x})$ constructed from a vector $\vec{x} = (x_{1}, x_{2},\dots,
x_{n})$ of positive real numbers, from a given set of spectral data. In
addition, we show that the spectrum of cell matrices $D(\vec{x})$ and
$D(\pi(\vec{x}))$ are the same, for every permutation $\pi \in S_{n}$.
