{"paper":{"title":"Perturbing eigenvalues of non-negative matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Chi-Kwong Li, Xuefeng Wang, Yiu-Tung Poon","submitted_at":"2014-02-05T00:53:22Z","abstract_excerpt":"Let $A$ be an irreducible (entrywise) nonnegative $n\\times n$ matrix with eigenvalues $$\\rho, b+ic,b-ic, \\lambda_4,\\cdots,\\lambda_n,$$ where $\\rho$ is the Perron eigenvalue. It is shown that for any $t \\in [0, \\infty)$ there is a nonnegative matrix with eigenvalues $$\\rho+ \\tilde t,\\lambda_2+t,\\lambda_3+t, \\lambda_4 \\cdots,\\lambda_n,$$ whenever $\\tilde t \\ge \\gamma_n t$ with $\\gamma_3=1, \\gamma_4 = 2, \\gamma_5=\\sqrt 5$ and $\\gamma_n = 2.25$ for $n \\ge 6$. The result improves that of Guo et al. Our proof depends on an auxiliary result in geometry asserting that the area of an $n$-sided convex p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0917","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"}