{"paper":{"title":"Relation between the T-congruence Sylvester equation and the generalized Sylvester equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Masaya Oozawa, Shao-Liang Zhang, Tomohiro Sogabe, Tomoya Kemmochi, Yuki Satake, Yuto Miyatake","submitted_at":"2019-03-13T08:47:25Z","abstract_excerpt":"The T-congruence Sylvester equation is the matrix equation $AX+X^{\\mathrm{T}}B=C$, where $A\\in\\mathbb{R}^{m\\times n}$, $B\\in\\mathbb{R}^{n\\times m}$, and $C\\in\\mathbb{R}^{m\\times m}$ are given, and $X\\in\\mathbb{R}^{n\\times m}$ is to be determined. Recently, Oozawa et al. discovered a transformation that the matrix equation is equivalent to one of the well-studied matrix equations (the Lyapunov equation); however, the condition of the transformation seems to be too limited because matrices $A$ and $B$ are assumed to be square matrices ($m=n$). In this paper, two transformations are provided for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05360","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"}