English

Row Cones, Perron Similarities, and Nonnegative Spectra

Spectral Theory 2018-08-15 v1

Abstract

In further pursuit of the diagonalizable \emph{real nonnegative inverse eigenvalue problem} (RNIEP), we study the relationship between the \emph{row cone} Cr(S)\mathcal{C}_r(S) and the \emph{spectracone} C(S)\mathcal{C}(S) of a Perron similarity SS. In the process, a new kind of matrix, \emph{row Hadamard conic} (RHC), is defined and related to the D-RNIEP. Characterizations are given when Cr(S)=C(S)\mathcal{C}_r(S) = \mathcal{C}(S), and explicit examples are given for all possible set-theoretic relationships between the two cones. The symmetric NIEP is the special case of the D-RNIEP in which the Perron similarity SS is also orthogonal.

Keywords

Cite

@article{arxiv.1611.02752,
  title  = {Row Cones, Perron Similarities, and Nonnegative Spectra},
  author = {C. R. Johnson and Pietro Paparella},
  journal= {arXiv preprint arXiv:1611.02752},
  year   = {2018}
}
R2 v1 2026-06-22T16:46:30.540Z