{"paper":{"title":"Non-commutative Edmonds' problem and matrix semi-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AC","math.RA"],"primary_cat":"cs.DS","authors_text":"G\\'abor Ivanyos, K. V. Subrahmanyam, Youming Qiao","submitted_at":"2015-08-04T07:39:16Z","abstract_excerpt":"In 1967, Edmonds introduced the problem of computing the rank over the rational function field of an $n\\times n$ matrix $T$ with integral homogeneous linear polynomials. In this paper, we consider the non-commutative version of Edmonds' problem: compute the rank of $T$ over the free skew field. It is known that this problem relates to the ring of matrix semi-invariants. In particular, if the nullcone of matrix semi-invariants is defined by elements of degree $\\leq \\sigma$, then there follows a $\\mathrm{poly}(n, \\sigma)$-time randomized algorithm to decide whether the non-commutative rank of $T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00690","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"}