{"paper":{"title":"Commutation principles in Euclidean Jordan algebras and normal decomposition systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.RA","authors_text":"Juyoung Jeong, M. Seetharama Gowda","submitted_at":"2016-04-15T16:37:38Z","abstract_excerpt":"The commutation principle of Ramirez, Seeger, and Sossa \\cite{ramirez-seeger-sossa} proved in the setting of Euclidean Jordan algebras says that when the sum of a Fr\\'{e}chet differentiable function $\\Theta(x)$ and a spectral function $F(x)$ is minimized over a spectral set $\\Omega$, any local minimizer $a$ operator commutes with the Fr\\'{e}chet derivative $\\Theta^{\\prime}(a)$. In this paper, we extend this result to sets and functions which are (just) invariant under algebra automorphisms. We also consider a similar principle in the setting of normal decomposition systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04561","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"}