{"paper":{"title":"The equality of generalized matrix functions on the set of all symmetric matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kijti Rodtes, Ratsiri Sanguanwong","submitted_at":"2018-08-30T15:03:50Z","abstract_excerpt":"A generalized matrix function $d_\\chi^G : M_n(\\mathbb{C}) \\rightarrow \\mathbb{C}$ is a function constructed by a subgroup $G$ of $S_n$ and a complex valued function $\\chi$ of $G$.\n  The main purpose of this paper is to find a necessary and sufficient condition for the equality of two generalized matrix functions on the set of all symmetric matrices, $\\mathbb{S}_n(\\mathbb{C})$.\n  In order to fulfill the purpose, a symmetric matrix $S_\\sigma$ is constructed and $d_\\chi^G(S_\\sigma)$ is evaluated for each $\\sigma \\in S_n$.\n  By applying the value of $d_\\chi^G(S_\\sigma)$, it is shown that $d_\\chi^G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10338","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"}