{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:XYOEM2XVX54D245HVW5GQSGRMU","short_pith_number":"pith:XYOEM2XV","schema_version":"1.0","canonical_sha256":"be1c466af5bf783d73a7adba6848d1651f3a71f185280d6914b2ca3753bf9146","source":{"kind":"arxiv","id":"math-ph/9811003","version":1},"attestation_state":"computed","paper":{"title":"Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle","license":"","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"R. Simon, S. Chaturvedi, V. Srinivasan","submitted_at":"1998-11-04T09:40:06Z","abstract_excerpt":"It is shown that a $N\\times N$ real symmetric [complex hermitian] positive definite matrix $V$ is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in $SO(m,n)$ [ $SU(m,n)$], for any choice of partition $N=m+n$. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson's theorem which states that if $N$ is even then $V$ is congruent also to a diagonal matrix modulo a symplectic matrix in $Sp(N,{\\cal R})$ [$Sp(N,{\\cal C})$]. Applications of these results considered include a generalization of "},"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":"math-ph/9811003","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1998-11-04T09:40:06Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"89055c2701fd1625a023ebd174c8d9a17034c1403aec3d8a92e56b767d59b2a4","abstract_canon_sha256":"30bed039758e2725670aab5117fccf18b9fb33a9a04d58f9c363cdf049942239"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:30.678152Z","signature_b64":"G/Rm80w/h9eVm/ORcOuWReHp7TW2TqnSNHjNt7FRLksJydyUIrK1K3nbD5EDDxA5QA5WezCWqCDWcgP9l+2ZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be1c466af5bf783d73a7adba6848d1651f3a71f185280d6914b2ca3753bf9146","last_reissued_at":"2026-05-18T01:38:30.677773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:30.677773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle","license":"","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"R. Simon, S. Chaturvedi, V. Srinivasan","submitted_at":"1998-11-04T09:40:06Z","abstract_excerpt":"It is shown that a $N\\times N$ real symmetric [complex hermitian] positive definite matrix $V$ is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in $SO(m,n)$ [ $SU(m,n)$], for any choice of partition $N=m+n$. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson's theorem which states that if $N$ is even then $V$ is congruent also to a diagonal matrix modulo a symplectic matrix in $Sp(N,{\\cal R})$ [$Sp(N,{\\cal C})$]. Applications of these results considered include a generalization of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9811003","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":"math-ph/9811003","created_at":"2026-05-18T01:38:30.677827+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9811003v1","created_at":"2026-05-18T01:38:30.677827+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9811003","created_at":"2026-05-18T01:38:30.677827+00:00"},{"alias_kind":"pith_short_12","alias_value":"XYOEM2XVX54D","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"XYOEM2XVX54D245H","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"XYOEM2XV","created_at":"2026-05-18T12:25:49.038998+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2408.04894","citing_title":"On generalization of Williamson's theorem to real symmetric matrices","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU","json":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU.json","graph_json":"https://pith.science/api/pith-number/XYOEM2XVX54D245HVW5GQSGRMU/graph.json","events_json":"https://pith.science/api/pith-number/XYOEM2XVX54D245HVW5GQSGRMU/events.json","paper":"https://pith.science/paper/XYOEM2XV"},"agent_actions":{"view_html":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU","download_json":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU.json","view_paper":"https://pith.science/paper/XYOEM2XV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/9811003&json=true","fetch_graph":"https://pith.science/api/pith-number/XYOEM2XVX54D245HVW5GQSGRMU/graph.json","fetch_events":"https://pith.science/api/pith-number/XYOEM2XVX54D245HVW5GQSGRMU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU/action/storage_attestation","attest_author":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU/action/author_attestation","sign_citation":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU/action/citation_signature","submit_replication":"https://pith.science/pith/XYOEM2XVX54D245HVW5GQSGRMU/action/replication_record"}},"created_at":"2026-05-18T01:38:30.677827+00:00","updated_at":"2026-05-18T01:38:30.677827+00:00"}