{"paper":{"title":"Numerical Ranges of KMS Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hwa-Long Gau, Pei Yuan Wu","submitted_at":"2013-04-01T04:30:04Z","abstract_excerpt":"A KMS matrix is one of the form $$J_n(a)=[{array}{ccccc} 0 & a & a^2 &... & a^{n-1} & 0 & a & \\ddots & \\vdots & & \\ddots & \\ddots & a^2 & & & \\ddots & a 0 & & & & 0{array}]$$ for $n\\ge 1$ and $a$ in $\\mathbb{C}$. Among other things, we prove the following properties of its numerical range: (1) $W(J_n(a))$ is a circular disc if and only if $n=2$ and $a\\neq 0$, (2) its boundary $\\partial W(J_n(a))$ contains a line segment if and only if $n\\ge 3$ and $|a|=1$, and (3) the intersection of the boundaries $\\partial W(J_n(a))$ and $\\partial W(J_n(a)[j])$ is either the singleton $\\{\\min\\sigma(\\re J_n(a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0295","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"}