{"paper":{"title":"A simultaneous decomposition of four real quaternion matrices encompassing $\\eta$-Hermicity 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":"2017-02-02T06:35:16Z","abstract_excerpt":"Let $\\mathbb{H}$ be the real quaternion algebra and $\\mathbb{H}^{m\\times n}$ denote the set of all $m\\times n$ matrices over $\\mathbb{H}$. Let $\\mathbf{i},\\mathbf{j},\\mathbf{k}$ be the imaginary quaternion units. For $\\eta\\in\\{\\mathbf{i},\\mathbf{j},\\mathbf{k}\\}$, a square real quaternion matrix $A$ is said to be $\\eta$-Hermitian if $A^{\\eta*}=A$ where $A^{\\eta*}=-\\eta A^{\\ast}\\eta$, and $A^{\\ast}$ stands for the conjugate transpose of $A$. In this paper, we construct a simultaneous decomposition of four real quaternion matrices with the same row number $(A,B,C,D),$ where $A=A^{\\eta*}\\in \\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00551","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"}