Kernel structure of Toeplitz-plus-Hankel matrices Original Research Article

The structure of the kernel of block Toeplitz-plus-Hankel matrices R=[aj−k+bj+k], where aj and bj are the given p×q blocks with entries from a given field, is investigated. It is shown that R corresponds to two systems of at most p+q vector polynomials from which a basis of the kernel of R and all other Toeplitz-plus-Hankel matrices with the same parameters aj and bj can be built. The main result is an analogue of a known kernel structure theorem for block Toeplitz and block Hankel matrices.