Extreme nonnegative matrices Original Research Article

An (entrywise) nonnegative n × n matrix A is extreme if its spectrum (λ1,…, λn) has the property that for all ε > 0, (λ1 − ε,…, λn − ε) is not the spectrum of a nonnegative matrix. It is proved that if A is an extreme nonnegative matrix, then there exists a nonzero nonnegative matrix Y such that AY = YA and AT ring operator Y = 0 where ring operator is the Hadamard (or entrywise) product and T denotes transpose.