Generating polynomials for matrices with Toeplitz or conjugate-Toeplitz inverses

A complex matrix A = a_ij] has been called conjugate-Toeplitz if a_ij = c^i?1(a_i?j), where c( ) denotes conjugation. A necessary and sufficient condition is derived for a matrix H to have a conjugate-Toeplitz inverse. The elements of H are generated from the coefficients of certain polynomials. The result is simplified either when H is to have a Toeplitz inverse, or when H is banded and is to have a conjugate-Toeplitz inverse. Each of these consequences of the main theorem is a different generalization of a previous result on banded matrices having a Toeplitz inverse.