An Inverse Eigenvalue Problem for Symmetric Arrow-Plus-Jacobi Matrices

In this paper we study a kind of inverse eigenvalue problem for a special kind of real symmetric matrices: the real symmetric Arrow-plus-Jacobi matrices. That is, matrices which look like arrow matrices forward and Jacobi backward, from the( p, p )station, 1 ≤p ≤ n. We give a necessary and sufficient condition for the existence of such a matrix. Our results are constructive, in the sense that they generate an algorithmic procedure to construct the matrix.