In [3] K. Goldberg showed that if A is a 0-1 matrix that satisfies(1.1)then for some permutation matrix P, PAP* is a direct sum of matrices each of
which is either zero or consists only of ones. More recently J. L. Brenner
[1] proved that if A ∦ 0 (i.e. A has non-negative entries) and satisfies (1)
then there exists a permutation matrix P such that PAP* = A1⊕ …
⊕An in in which each Ai is either 0 or all
positive, Ai > 0, and satisfies (1) as well.