Perfect and Ideal 0, ±1 Matrices

A 0, ±1 matrix A is said to be perfect (resp. ideal) if the corresponding generalized packing (resp. covering) polytope is integral. Given a 0, ±1 matrix A, we construct a 0, 1 matrix that is perfect if and only if A is perfect. A similar result is obtained for the generalized covering problem. We also extend some known results on perfect 0, 1 matrices to the 0, ±1 case.