A common characterization of M-matrices are non-singular square matrices with non-positive off-diagonal entries, positive diagonal entries, non-negative row sums, and at least one positive row sum
It seems that this characterization depends on the use of rows or columns. I don't understand how that is possible, as the transposed of an M-Matrix is also an M-Matrix.
Example: $\left( \begin{array}{ccc} 2 & -1 &0\\ -2 & 2&-1\\ 0&-1&2 \end{array} \right)$
This matrix is not diagonally dominant, but its transpose is.
However the matrix is clearly M-Matrix, because all Eigenvalues are positive.
Thanks for your help!