2020/03/18 by Ana I. Julio, Julio, Ana I., Ricardo L. Soto +1
Chemistry · Computer Science · Mathematics · #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Molecular spectroscopy and chirality #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2003.08722
openalex publication_date 2020/03/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We say that a list \Λ = \λ 1,\… ,\λ n of\ncomplex numbers is realizable, if it is the spectrum of a nonnegative matrix\nA (the realizing matrix). We say that \Λ is universally realizable if\nit is realizable for each possible Jordan canonical form allowed by \Λ\n. This work does not contain new results. As its title says, our goal is to\nshow and emphasize the relevance of certain results of Brauer and Rado in the\nstudy of nonnegative inverse spectral problems. We show that virtually all\nknown results, which give sufficient conditions for the list \Λ to be\nrealizable or universally realizable, can be obtained from the results of\nBrauer or Rado. Moreover, in this case, we may always compute a realizing\nmatrix.\n