An inverse eigenvalue problem for modified pseudo-Jacobi matrices

In this paper, we investigate an inverse eigenvalue problem for matrices that are obtained from pseudo-Jacobi matrices by only modifying the (1,r)-th and (r,1)-th entries, 3≤r≤n. Necessary and sufficient conditions under which the problem is solvable are derived. Uniqueness results are presented and an algorithm to reconstruct the matrices from the given spectral data is proposed. Illustrative examples are provided.