Spectrally Simple Spectra without Irreducible Nonnegative Realizations
2026-10-09
Research publication
Spectrally Simple Spectra without Irreducible Nonnegative Realizations
Preprint
- Original date
- Authors
- Yair Lavi
- Matrix theory
- Nonnegative matrices
- Nonnegative inverse eigenvalue problem
Abstract
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.