Centrosymmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices and Bezoutians

AbstractIn the paper algebraic properties of centrosymmetric and centro-skewsymmetric Toeplitz-plus-Hankel (T+H) matrices are investigated. It is shown that in the nonsingular case the inverse can be constructed with the help of the solutions of four related Toeplitz systems with symmetric or skewsymmetric right-hand sides. In the singular case the related Toeplitz matrices determine the kernel of the T+H matrices. Finally centrosymmetric and centro-skewsymmetric T+H Bezoutians are characterized