Inverse eigenvalue problem for matrices whose graph is a banana tree

Abstract

In this paper, we consider an inverse eigenvalue problem (IEP) for constructing a special kind of acyclic matrices. The problem involves the reconstruction of matrices whose graph is a banana tree. This is performed by using the minimal and maximal eigenvalues of all leading principal submatrices of the required matrix. The necessary and sufficient conditions<br />for the solvability of the problem is derived. An algorithm to construct the solution is provided.