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arXiv · 1611.02752

Row Cones, Perron Similarities, and Nonnegative Spectra

C. R. Johnson·Pietro Paparella
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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.

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BibTeXRIS

C. R. Johnson, Pietro Paparella. 2016-11-08. Row Cones, Perron Similarities, and Nonnegative Spectra. https://doi.org/10.1080/03081087.2017.1329269

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