Diagonalizably realizable implies universally realizable (Q6628847)

This paper studies a question belonging to the Nonnegative Inverse Eigenvalue Problem (NIEP): when does diagonalizable realizability (DR) of a spectrum imply universal realizability (UR)? The authors establish that DR spectra are UR under specific conditions, enhancing the theoretical understanding of nonnegative matrix spectra. They prove that DR spectra imply UR for particular Jordan structures, addressing a question open since \textit{H. Minc}'s work in 1981 [Proc. Am. Math. Soc. 83, 665--669 (1981; Zbl 0472.15006)]. This result connects the properties of DR matrices with universal realizability and deepens the theoretical understanding of nonnegative matrix spectra.\N\NThe authors make use of recent advances in matrix perturbation and similarity to provide a path from DR to UR, supported by examples that include both non-extreme and extreme spectra cases.