We fully characterize the class of totally positive matrices whose inverses are M-matrices, improving upon the characterization given by Markham. We also characterize the set of M-matrices whose inverses are totally positive, and show that this set is formed by the tridiagonal M-matrices. © 1995.
Peña, J. M. (1995). M-matrices whose inverses are totally positive. Linear Algebra and Its Applications, 221(C), 189–193. https://doi.org/10.1016/0024-3795(93)00244-T