Abstract
An (entrywise) nonnegative n × n matrix A is extreme if its spectrum ( λ 1,…, λ n ) has the property that for all ϵ > 0, ( λ 1 − ϵ,…, λ n − 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 A T ∘ Y = 0 where ∘ is the Hadamard (or entrywise) product and T denotes transpose.
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