2023/01/11 by Charles R. Johnson, Johnson, Charles R., Ana I. Julio +3
Agricultural and Biological Sciences · Mathematics · #Advanced Scientific Research Methods #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2301.04701
openalex publication_date 2023/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A list Λ=\λ1,… ,λn\ of complex numbers (repeats allowed) is said to be realizable if it is the spectrum of an entrywise nonnegative matrix A. Λ is diagonalizably realizable if the realizing matrix A is diagonalizable. Λ is said to be universally realizable if it is realizable for each possible Jordan canonical form allowed by Λ. Here, we study the connection between diagonalizable realizability and universal realizability of spectra. In particular, we establish indices of realizability for diagonalizable and universal realizability. We also define the merge of two spectra and we prove a result that allow us to easily decide, in many cases, about the universal realizability of spectra.