On the Eigenstructure of Hermitian Toeplitz Matrices with Prescribed Eigenpairs

Toeplitz matrices have found important applications in bioinformatics and computational biology [5, 6, 11, 12]. In this paper we concern the spectral properties of hermitian Toeplitz matrices. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformation, we first consider the eigenstructure of hermitian Toeplitz matrices and then discuss a related inverse eigenproblem. We show that the dimension of the subspace of hermitian Toeplitz matrices with two given eigenvectors is at least two and independent of the size of the matrix, the solution of the inverse hermitian Toeplitz eigenproblem with two given eigenpairs is unique.