{"paper":{"title":"Inequalities on generalized matrix functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chi-Kwong Li, Qing-Wen Wang, Shaowu Huang, Yiu-Tung Poon","submitted_at":"2016-05-23T11:54:08Z","abstract_excerpt":"We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number $r \\in \\{1\\} \\cup [2, \\infty)$, positive semi-definite matrices $A_i,\\ B_i,\\ C_i\\in M_{n_i}$, $i=1,2$, and generalized matrix functions $d_\\chi, d_\\xi$ such as the determinant and permanent, etc., we have \\begin{eqnarray*}&&\\left(d_\\chi(A_1+B_1+C_1)d_\\xi(A_2+B_2+C_2)\\right)^r \\\\ &&\\hskip 1in\n  + \\left(d_\\chi(A_1)d_\\xi(A_2)\\right)^r\n  + \\left(d_\\chi(B_1)d_\\xi(B_2)\\right)^r + \\left(d_\\chi(C_1)d_\\xi(C_2)\\right)^r \\\\ & \\ge &\\left("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06984","kind":"arxiv","version":2},"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"}