{"paper":{"title":"Row Cones, Perron Similarities, and Nonnegative Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"C. R. Johnson, Pietro Paparella","submitted_at":"2016-11-08T22:39:24Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02752","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}