{"paper":{"title":"The radius in matrix algebras--Examples and remarks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Moshe Goldberg","submitted_at":"2015-11-09T16:04:58Z","abstract_excerpt":"The main purpose of this note is to illustrate how the radius in a finite-dimensional power-associative algebra over a field $\\mathbb{F}$, either $\\mathbb{R}$ or $\\mathbb{C}$, may change when the multiplication in this algebra is modified. Our point of departure will be $\\mathbb{F}^{n \\times n}$, the familiar algebra of $n \\times n$ matrices over $\\mathbb{F}$ with the usual matrix operations, where it is known that the radius is the classical spectral radius. We shall alter the multiplication in $\\mathbb{F}^{n \\times n}$ in three different ways and compute, in each case, the radius in the resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02732","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"}