{"paper":{"title":"Specht's criterion for systems of linear mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Roger A. Horn, Vladimir V. Sergeichuk, Vyacheslav Futorny","submitted_at":"2017-01-30T21:05:30Z","abstract_excerpt":"W.Specht (1940) proved that two $n\\times n$ complex matrices $A$ and $B$ are unitarily similar if and only if $\\operatorname{trace} w(A,A^{\\ast}) = \\operatorname{trace} w(B,B^{\\ast})$ for every word $w(x,y)$ in two noncommuting variables. We extend his criterion and its generalizations by N.A.Wiegmann (1961) and N.Jing (2015) to an arbitrary system $\\mathcal A$ consisting of complex or real inner product spaces and linear mappings among them. We represent such a system by the directed graph $Q(\\mathcal A)$, whose vertices are inner product spaces and arrows are linear mappings. Denote by $\\wid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08826","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"}