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Then $$|\\det A|\\le a|\\det A_{11}|\\cdot|\\det A_{22}|,$$ where $a=\\{{array}{l l}\n  2^{3m/2}, & \\text{if} m\\le n/3;\n  2^{n/2}, & \\text{if} n/3<m\\le n/2.\n  {array}.$ This improves a result of Ikramov."},"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":"1209.4949","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-22T01:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"06c29c35336aa0429eb395ee33308803181de1ba5b2a105d9606ad6e6e60c40e","abstract_canon_sha256":"2d3f7a3a14642f7a2fa4f558223656cc7c2c1dcef06f9a0b4b560f851c1754f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:04.152874Z","signature_b64":"HvJgEk2gOJqqyK0BXP55BCu311bieh+1RO2uxcZmNHub2XY+jHOjKXPG9MG600GuFS/T2AWmjbqdmYtHo7FaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b083316c40ec9b26a8ee5b0a106846b4b4dda7aabd44411c23b167a7ef1a4611","last_reissued_at":"2026-05-18T03:41:04.152383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:04.152383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fischer type determinantal inequalities for accretive-dissipative matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Minghua Lin","submitted_at":"2012-09-22T01:09:30Z","abstract_excerpt":"Let $A={bmatrix} A_{11} &A_{12} A_{21} & A_{22} {bmatrix}$ be an $n\\times n$ accretive-dissipative matrix, $k$ and l be the orders of $A_{11}$ and $A_{22}$, respectively, and let $m=\\min\\{k,l\\}$. Then $$|\\det A|\\le a|\\det A_{11}|\\cdot|\\det A_{22}|,$$ where $a=\\{{array}{l l}\n  2^{3m/2}, & \\text{if} m\\le n/3;\n  2^{n/2}, & \\text{if} n/3<m\\le n/2.\n  {array}.$ This improves a result of Ikramov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4949","kind":"arxiv","version":2},"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":"1209.4949","created_at":"2026-05-18T03:41:04.152457+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4949v2","created_at":"2026-05-18T03:41:04.152457+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4949","created_at":"2026-05-18T03:41:04.152457+00:00"},{"alias_kind":"pith_short_12","alias_value":"WCBTC3CA5SNS","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WCBTC3CA5SNSNKHO","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WCBTC3CA","created_at":"2026-05-18T12:27:25.539911+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/WCBTC3CA5SNSNKHOLMFBA2CGWS","json":"https://pith.science/pith/WCBTC3CA5SNSNKHOLMFBA2CGWS.json","graph_json":"https://pith.science/api/pith-number/WCBTC3CA5SNSNKHOLMFBA2CGWS/graph.json","events_json":"https://pith.science/api/pith-number/WCBTC3CA5SNSNKHOLMFBA2CGWS/events.json","paper":"https://pith.science/paper/WCBTC3CA"},"agent_actions":{"view_html":"https://pith.science/pith/WCBTC3CA5SNSNKHOLMFBA2CGWS","download_json":"https://pith.science/pith/WCBTC3CA5SNSNKHOLMFBA2CGWS.json","view_paper":"https://pith.science/paper/WCBTC3CA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4949&json=true","fetch_graph":"https://pith.science/api/pith-number/WCBTC3CA5SNSNKHOLMFBA2CGWS/graph.json","fetch_events":"https://pith.science/api/pith-number/WCBTC3CA5SNSNKHOLMFBA2CGWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WCBTC3CA5SNSNKHOLMFBA2CGWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WCBTC3CA5SNSNKHOLMFBA2CGWS/action/storage_attestation","attest_author":"https://pith.science/pith/WCBTC3CA5SNSNKHOLMFBA2CGWS/action/author_attestation","sign_citation":"https://pith.science/pith/WCBTC3CA5SNSNKHOLMFBA2CGWS/action/citation_signature","submit_replication":"https://pith.science/pith/WCBTC3CA5SNSNKHOLMFBA2CGWS/action/replication_record"}},"created_at":"2026-05-18T03:41:04.152457+00:00","updated_at":"2026-05-18T03:41:04.152457+00:00"}