Constructing a real symmetric Toeplitz matrix with two prescribed eigenpairs

This paper is concerned with the inverse eigenvalue problems for symmetric Toeplitz matrices. A kind of inverse problem for constructing a real symmetric Toeplitz matrix from the given k eigenpairs is proposed. By using the special structure of symmetric Toeplitz matrices, the Kronecker product and the vec operator of matrices, the problem is transformed into the system of linear equations. Some necessary and sufficient conditions for the solvability of the problem are given. The general solutions of the problem are presented.