Diagonal realizability in the Nonnegative Inverse Eigenvalue Problem

2018/05/17 by Thomas J. Laffey, Laffey, Thomas J., Helena Šmigoc +1
Computer Science · Engineering · Mathematics · #15B48 #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1805.06707

openalex publication_date 2018/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if a list of nonzero complex numbers σ=(λ₁,λ₂,…,λ_k) is the nonzero spectrum of a diagonalizable nonnegative matrix, then σ is the nonzero spectrum of a diagonalizable nonnegative matrix of order k+k².

Related

• Diagonal elements in the Nonnegative Inverse Eigenvalue Problem
• The diagonalizable nonnegative inverse eigenvalue problem
• The role of certain Brauer and Rado results in the nonnegative inverse\n spectral problems
• Constructing New Realisable Lists from Old in the NIEP
• A simplification of the C-realizability criterion for the Nonnegative Inverse Eigenvalue Problem for integers