On a class of equivalent systems of linear inequalities

d iS = d v = ^i + e m+j ) where v = n(i -1) + j e denoting the th unit vector in R m+n . It should be noted that D is of rank m + n -1: first, the subset of columns d il9 d 13 -(i = 1, 2, , m; j = 2, 3, , w) is independent, hence, the rank ^ m + n -1; second, if e -e + + m - m+1 -... -e w+% , then consideration of the inner products e f d i = 0, ' = 1 when i ^ m, e'i = -1 when i > m shows that, say, x is not representable in terms of columns of D, since e 1 = ^^ would imply 1 = ' l = 2 ii'd^ = 0.