EXTREME NONNEGATIVE MATRICES

An (entrywise) nonnegative n x n matrix A is extreme if its spectrum ( lambda(1),...,lambda(n)) has the property that for all epsilon > 0, (l ambda(1)-epsilon,...,lambda(n)-epsilon) is not the spectrum of a nonne gative matrix. It is proved that if A is an extreme nonnegative matrix , then there exists a nonzero nonnegative matrix Y such that AY = YA a nd A(T) circle Y = 0 where circle plus is the Hadamard (or entrywise) product and T denotes transpose. (C) 1998 Elsevier Science Inc. All ri ghts reserved.