{"paper":{"title":"Partial determinants of Kronecker products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Yorick Hardy","submitted_at":"2017-09-29T06:54:12Z","abstract_excerpt":"Let $\\det_2(A)$ be the block-wise determinant (partial determinant). We consider the condition for completing the determinant $\\det(\\det_2(A)) = \\det(A),$ and characterize the case for an arbitrary Kronecker product $A$ of matrices over an arbitrary field. Further insisting that $\\det_2(AB)=\\det_2(A)\\det_2(B)$, for Kronecker products $A$ and $B$, yields a multiplicative monoid of matrices. This leads to a determinant-root operation $\\text{Det}$ which satisfies $\\text{Det}(\\text{Det}_2(A)) = \\text{Det}(A)$ when $A$ is a Kronecker product of matrices for which $\\text{Det}$ is defined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10253","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"}