{"paper":{"title":"Two nondeterministic positive definiteness tests for unidiagonal integral matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Mr\\'oz","submitted_at":"2019-06-28T17:18:15Z","abstract_excerpt":"For standard algorithms verifying positive definiteness of a matrix $A\\in\\mathbb{M}_n(\\mathbb{R})$ based on Sylvester's criterion, the computationally pessimistic case is this when $A$ is positive definite. We present two algorithms realizing the same task for $A\\in\\mathbb{M}_n(\\mathbb{Z})$, for which the case when $A$ is positive definite is the optimistic one. The algorithms have pessimistic computational complexities $\\mathcal{O}(n^3)$ and $\\mathcal{O}(n^4)$ and they rely on performing certain edge transformations, called inflations, on the edge-bipartite graph (=bigraph) $\\Delta=\\Delta(A)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12312","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"}