Inverse Eigenvalue Problem for a Kind of Acyclic Matrices

Abstract

In this paper, we study an inverse eigenvalue problem for reconstruction of matrices whose graph is a double starlike tree. This is performed by using the minimal and maximal eigenvalues of all leading principal submatrices of the required matrix. The usual process of solving the problem involves the use of recurrence relations among the characteristic polynomials of the leading principal submatrices of $$\lambda I-A$$ where A is the required matrix. We investigate the necessary and sufficient conditions for the solvability of the problem. Finally, we provide an algorithm to construct the matrix.