On the Toeplitz embedding of an arbitrary matrix

Abstract

It has been shown by Delosme and Morf that an arbitrary block matrix can be embedded into a block Toeplitz matrix; the dimension of this embedding depends on the complexity of the matrix structure compared to the block Toeplitz structure. Due to the special form of the embedding matrix, the algebra of matrix polynomials relative to block Toeplitz matrices can be interpreted directly in terms of the original matrix and therefore can be extended to arbitrary matrices. In fact, these polynomials turn out to provide an appropriate framework for the recently proposed generalized Levinson algorithm solving the general matrix inversion problem.