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math.RA — Rings and Algebras

Spectrally Simple Spectra without Irreducible Nonnegative Realizations

Contributed by Yair Lavi

We give a counterexample to a conjecture of Johnson, Marijuán, and Pisonero: we show that the spectrum $\{1,1/2,\pm i/\sqrt3\}$ is realizable and spectrally simple, but has no irreducible nonnegative realization. More generally, we prove their nonexistence conjecture for an order-four boundary family.

A mix of human-written and AI-generated textHuman understanding: all partsIrreducible matricesIrreducible realizationNonnegative inverse eigenvalue problemPerron rootSpectrally simple spectrumnonnegative matrices

Nov 10, 20265 pages

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Spectrally Simple Spectra without Irreducible Nonnegative Realizations

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