{"paper":{"title":"Nondegenerate $2 \\times k \\times (k+1)$ Hypermatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.RT","authors_text":"Colin Aitken","submitted_at":"2016-06-14T04:17:47Z","abstract_excerpt":"We construct an extension of Gaussian elimination to show that if $\\mathbb{F}$ is a topological field, then there is a transitive, free, and continuous action of a natural quotient of $GL_k(\\mathbb{F}) \\times GL_{k+1}(\\mathbb{F})$ on the set $M_k(\\mathbb{F})$ of $2 \\times k \\times (k+1)$ hypermatrices over $\\mathbb{F}$ with nonzero hyperdeterminant.\n  We use this action to answer a number of questions including determining the homotopy groups of $M_k(\\mathbb{C})$, counting elements of $M_k(\\mathbb{F}_q)$ (generalizing an unpublished result of Lewis and Sam), and computing hyperdeterminants for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04532","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"}