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Johnson, C.R. and Paparella, P. (2016) Spectral Conditions for the Nonnegative Inverse Eigenvalue Problem. Linear Algebra and Its Applications, 505, 1-15.

has been cited by the following article:

• TITLE: A Generating-Function Perspective on a Nonrealizable Trace-Zero Spectrum of Nonnegative 5 × 5 Matrices

  AUTHORS: Bishnu P. Sedai

  KEYWORDS: Nonnegative Inverse Eigenvalue Problem, Trace-Zero Spectrum, Johnson-Loewy-London Inequality, Generating Functions

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.16 No.1, February 25, 2026

  ABSTRACT: We study a classical trace-zero spectrum that has played a central role in the analysis of the 5 × 5 nonnegative inverse eigenvalue problem. This spectrum is particularly illustrative because it fails to be realizable at the unperturbed parameter value, yet becomes realizable precisely once the symmetric perturbation exceeds a unique critical threshold. Using an exponential generating-function representation of power sums, we show that the refined Johnson-Loewy-London inequality is governed by a strictly increasing functional whose derivative is a polynomial in the perturbation parameter. This yields a transparent structural explanation of the sharp realizability threshold and recovers, in a unified way, earlier results of Salzmann, Friedland, and Laffey-Meehan. The method extends naturally to higher-order Johnson-Loewy-London inequalities and provides a convenient framework for analyzing parametrized families in the nonnegative inverse eigenvalue problem.