{"paper":{"title":"The asymptotic complexity of matrix reduction over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DS","authors_text":"Demetres Christofides","submitted_at":"2014-06-23T08:03:23Z","abstract_excerpt":"Consider an invertible n \\times n matrix over some field. The Gauss-Jordan elimination reduces this matrix to the identity matrix using at most n^2 row operations and in general that many operations might be needed.\n  In [1] the authors considered matrices in GL(n;q), the set of n \\times n invertible matrices in the finite field of q elements, and provided an algorithm using only row operations which performs asymptotically better than the Gauss-Jordan elimination. More specifically their `striped elimination algorithm' has asymptotic complexity \\frac{n^2}{\\log_q{n}}. Furthermore they proved t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5826","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"}