For an (m × n)-matrix A the set C(A) is studied containing the constraint vectors b of ℝm without strongly redundant inequalities in the system (Ax ≤ b, x ≥ 0). C(A) is a polyhedral cone containing as a subset the cone Col(A) generated by the column vectors of A. This paper characterizes the matrices A for which the equality C(A) = Col(A) holds. Furthermore, the matrices A are characterized for which C(A) is generated by those constraint vectors βi ∈ C(A), i ∈ {1, 2, . . . , m}, for which the feasible region {x ∈ ℝn+: Ax ≤ βi} equals {x ∈ ℝn+: (Ax)i ≤ 1}. Necessary conditions are formulated for a constraint vector to be an element of C(A). The class of matrices is characterized for which these conditions are also sufficient.
