{"paper":{"title":"A simultaneous decomposition of seven matrices over real quaternion algebra and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Qing-Wen Wang, Zhuo-Heng He","submitted_at":"2014-09-04T14:38:51Z","abstract_excerpt":"Let $\\mathbb{H}$ be the real quaternion algebra and $\\mathbb{H}^{n\\times m}$ denote the set of all $n\\times m$ matrices over $\\mathbb{H}$. In this paper, we construct a simultaneous decomposition of seven general real quaternion matrices with compatible sizes: $A\\in \\mathbb{H}^{m\\times n}, B\\in \\mathbb{H}^{m\\times p_{1}},C\\in \\mathbb{H}^{m\\times p_{2}},D\\in \\mathbb{H}^{m\\times p_{3}},E\\in \\mathbb{H}^{q_{1}\\times n},F\\in \\mathbb{H}^{q_{2}\\times n},G\\in \\mathbb{H}^{q_{3}\\times n}$. As applications of the simultaneous matrix decomposition, we give solvability conditions, general solutions, as wel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1453","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"}