Characterisation and properties of r-Toeplitz matrices

AbstractAn r-Toeplitz (rT) matrix can be regarded as a block Toeplitz matrix with order some multiple of r from which a bottom border and a right-hand border have been removed. It is shown that some known properties of Toeplitz matrices extend to this new class. In particular, a necessary and sufficient condition is given, in terms of a linear matrix equation, for a nonsingular matrix to have rT form, from which it follows that the elements of the inverse are completely determined by those in its first and last r rows and columns. In addition, some results are presented for cases when the inverse of an rT matrix has certain banded forms