Inverse eigenvalue problem of bisymmetric nonnegative matrices

Abstract

This paper considers an inverse eigenvalue problem for‎ bisymmetric nonnegative matrices‎. ‎We first discuss the specified‎ structure of the bisymmetric matrices‎. ‎Then for a given set of real‎ numbers of order maximum ‎‎five‎ with special conditions‎, ‎we construct‎ a nonnegative bisymmetric matrix such that the given set is its spectrum‎‎. ‎Finally, we solve the problem for ‎arbitrary ‎order $n$ in the special case of the spectrum‎.