It is shown that a square band matrix H=(hij) with hij=0 for j- i>r and i-j>s, where r+s is less than the order of the matrix, has a Toeplitz inverse if and only if it has a special structure characterized by two polynomials of degrees r and s, respectively. © 1979.
Greville, T. N. E., & Trench, W. F. (1979). Band matrices with Toeplitz inverses. Linear Algebra and Its Applications, 27(C), 199–209. https://doi.org/10.1016/0024-3795(79)90042-9