{"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"}