The paper gives new observations on irreducible nonnegative realizations of realizable spectra and characterizes the trace-zero case via graph theory, plus related positive realizations.
Perfect, On positive stochastic matrices with real characteristic roots,Proceedings of the Cambridge Philosophical Society, 48 (1952) 271-276
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The INIEP: Irreducible and Positive Realizations
The paper gives new observations on irreducible nonnegative realizations of realizable spectra and characterizes the trace-zero case via graph theory, plus related positive realizations.