{"paper":{"title":"Determinants of Block Matrices with Noncommuting Blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Nat Sothanaphan","submitted_at":"2018-05-15T20:29:30Z","abstract_excerpt":"Let $M$ be an $mn\\times mn$ matrix over a commutative ring $R$. Divide $M$ into $m \\times m$ blocks. Assume that the blocks commute pairwise. Consider the following two procedures: (1) Evaluate the $n \\times n$ determinant formula at these blocks to obtain an $m \\times m$ matrix, and take the determinant again to obtain an element of $R$; (2) Take the $mn \\times mn$ determinant of $M$. It is known that the two procedures give the same element of $R$. We prove that if only certain pairs of blocks of $M$ commute, then the two procedures still give the same element of $R$, for a suitable definiti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06027","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"}