{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:XXF3ZGHQ2PDTJN2ZN6VRKLDRZI","short_pith_number":"pith:XXF3ZGHQ","schema_version":"1.0","canonical_sha256":"bdcbbc98f0d3c734b7596fab152c71ca0149df471c099f0eae48e8a495572ab8","source":{"kind":"arxiv","id":"1903.05360","version":1},"attestation_state":"computed","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1903.05360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-13T08:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"27b753e75e4bd67a584d837e331c01d80f5eaf6bda0d1acae937f78b8fa9cab1","abstract_canon_sha256":"ddeaa7838659be1bd4b55c8bb4c745f20355d7c903b8242b9e29186e431cf3ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:56.214611Z","signature_b64":"uBNUqpKxzZuLfaDlDSgBCA2unvpWVr1cwk61LmRhc5Faicf8knz1ACaVEKN1X5/Z0bLil3eeUA3l3zgCZoxYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdcbbc98f0d3c734b7596fab152c71ca0149df471c099f0eae48e8a495572ab8","last_reissued_at":"2026-05-17T23:43:56.213844Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:56.213844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1903.05360","created_at":"2026-05-17T23:43:56.213981+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.05360v1","created_at":"2026-05-17T23:43:56.213981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05360","created_at":"2026-05-17T23:43:56.213981+00:00"},{"alias_kind":"pith_short_12","alias_value":"XXF3ZGHQ2PDT","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"XXF3ZGHQ2PDTJN2Z","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"XXF3ZGHQ","created_at":"2026-05-18T12:33:33.725879+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI","json":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI.json","graph_json":"https://pith.science/api/pith-number/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/graph.json","events_json":"https://pith.science/api/pith-number/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/events.json","paper":"https://pith.science/paper/XXF3ZGHQ"},"agent_actions":{"view_html":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI","download_json":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI.json","view_paper":"https://pith.science/paper/XXF3ZGHQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.05360&json=true","fetch_graph":"https://pith.science/api/pith-number/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/graph.json","fetch_events":"https://pith.science/api/pith-number/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/action/storage_attestation","attest_author":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/action/author_attestation","sign_citation":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/action/citation_signature","submit_replication":"https://pith.science/pith/XXF3ZGHQ2PDTJN2ZN6VRKLDRZI/action/replication_record"}},"created_at":"2026-05-17T23:43:56.213981+00:00","updated_at":"2026-05-17T23:43:56.213981+00:00"}