A note on conjugate Toeplitz matrices (Q917651)

Based on elementary results about arbitrary partioned matrices, the authors propose an expression for the elements inside the inverse matrix of an r-Toeplitz and a conjugate Toeplitz matrix. A necessary condition for the application of the generalized Trench algorithm developed by \textit{S. Barnett} and \textit{M. J. C. Gover} [Linear Multilinear Algebra 14, 45- 65 (1983; Zbl 0536.15011)] is discussed. It follows a contradiction of an assertion of the same authors [J. Math. Anal. Appl. 100, 339-353 (1984; Zbl 0547.65022)].