Recovery of certain displacement matrices

There are various ways to prove that, under suitable conditions, the inverse of a Toeplitz matrix can be completely recovered from two of its columns. Toeplitz matrices and their inverses are matrices with displacement structure, i.e., they can be related with matrices of low rank via suitable linear operators. In this note, we show a possible generalization of the result concerning Toeplitz inverses for certain classes of matrices with displacement structure.