Inverse Eigenvalue Problem of Cell Matrices

Abstract

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 $\pi \in S_n$.

arXiv comment10 pages