{"paper":{"title":"Heron-Wasserstein majorization inequalities for spectral and Kubo-Ando geometric means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anh Thi Nguyen, Trung Dung Vuong, Trung Hoa Dinh","submitted_at":"2026-05-22T15:06:04Z","abstract_excerpt":"We prove sharp Heron-type majorization inequalities for two quadratic matrix expressions associated with the spectral and Kubo-Ando geometric means. For the spectral geometric mean cross term, we show that \\[ \\lambda\\bigl(a^2A+b^2B+c(A\\natural B)\\bigr) \\prec_w \\lambda\\bigl(W_{a,b}(A,B)\\bigr), \\qquad 0\\le c\\le 2ab, \\] where $W_{a,b}(A,B)$ is the weighted Bures-Wasserstein expression. The coefficient $2ab$ is sharp, and at this endpoint the weak majorization becomes majorization. For the Kubo-Ando geometric mean, we prove the direct comparison \\[ \\lambda\\bigl(a^2A+b^2B+2ab(A\\#B)\\bigr) \\prec_w \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26141","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26141/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}