Assume $X$ is a non-singular M-matrix. If all elements of $X$ are nonzero ($x_{ij}\neq 0, \forall i,j$), can I prove that $Y = X^{-1}$ is elementwise positive, $y_{ij}>0, \forall i,j$? If not, can anyone think of a sufficient condition(s) that would guarantee that all elements of the inverse of a non-singular M-matrix are positive?
2026-03-25 01:27:56.1774402076
Are there any sufficient conditions for a non-singular M-matrix to have an inverse with all-positive elements?
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