Summary: Fourier-Motzkin elimination is a classical method for solving linear inequalities in which one variable is eliminated in each iteration. This method is considered here as a matrix operation and properties of this operation are established. In particular, the focus is on situations where this matrix operation preserves combinatorial matrices (defined here as (0, 1, -1)-matrices).

05C50, 15A39, 90C27

linear inequalities, Fourier-Motzkin elimination, network matrices