Row Cones, Perron Similarities, and Nonnegative Spectra

Abstract

In further pursuit of the diagonalizable \emph{real nonnegative inverse eigenvalue problem} (RNIEP), we study the relationship between the \emph{row cone} ${\mathcal{C}}_r(S)$ and the \emph{spectracone} $\mathcal{C}(S)$ of a Perron similarity $S$. 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 ${\mathcal{C}}_r(S)=\mathcal{C}(S)$, 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 $S$ is also orthogonal.

References in corpus (2)

• Perron Spectratopes and the Real Nonnegative Inverse Eigenvalue Problem
• Realizing Suleimanova Spectra via Permutative Matrices

Cited by in corpus (2)

• Perron similarities and the nonnegative inverse eigenvalue problem
• Character tables are ideal Perron similarities