{"paper":{"title":"R-Orbit Reflexive Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Don Hadwin, Hassan Yousefi, Ileana Ionascu","submitted_at":"2011-12-08T18:30:41Z","abstract_excerpt":"We completely characterize orbit reflexivity and R-orbit reflexivity for square matrices over the real numbers. Unlike the complex case in which every matrix is orbit reflexive and C-orbit reflexivity is characterized solely in terms of the Jordan form, the orbit reflexivity and R-orbit reflexivity of a real matrix is described in terms of the linear dependence over Q of certain elements of R/Q. We also show that every n-by-n matrix over an uncountable field F is algebraically F-orbit reflexive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1904","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"}