{"paper":{"title":"Upper bound of typical ranks of m x n x ((m-1)n-1) tensors over the real number field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Mitsuhiro Miyazaki, Toshio Sakata, Toshio Sumi","submitted_at":"2013-04-26T19:31:15Z","abstract_excerpt":"Let $3\\leq m\\leq n$. We study typical ranks of $m\\times n\\times ((m-1)n-1)$ tensors over the real number field. The number $(m-1)n-1$ is a minimal typical rank of $m\\times n\\times ((m-1)n-1)$ tensors over the real number field. We show that a typical rank of $m\\times n\\times ((m-1)n-1)$ tensors over the real number field is less than or equal to $(m-1)n$ and in particular, $m\\times n\\times ((m-1)n-1)$ tensors over the real number field has two typical ranks $(m-1)n-1, (m-1)n$ if $m\\leq \\rho(n)$, where $\\rho$ is the Hurwitz-Radon function defined as $\\rho(n)=2^b+8c$ for nonnegative integers $a,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7260","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"}