{"paper":{"title":"On the Determinants and Inverses of Circulant Matrices with Pell and Pell-Lucas Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Durmu\\c{s} Bozkurt, Fatih Y{\\i}lmaz","submitted_at":"2012-01-29T17:19:03Z","abstract_excerpt":"Let P=\\circ(P_{1},P_{2},...,P_{n}) and Q=\\circ(Q_{1},Q_{2},...,Q_{n}) be n\\timesn circulant matrices where P_{n} and Q_{n} are nth Pell and Pell-Lucas numbers, respectively. The determinants of the matrices P and Q were expressed by the Pell and Pell-Lucas numbers. After, we prove that the matrices P and Q are the invertible for n\\geq3 and then the inverses of the matrices P and Q are derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6061","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"}