{"paper":{"title":"Typical rank of $m\\times n\\times (m-1)n$ tensors with $3\\leq m\\leq n$ 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":"2012-10-25T01:15:37Z","abstract_excerpt":"Tensor type data are used recently in various application fields, and then a typical rank is important. Let $3\\leq m\\leq n$. We study typical ranks of $m\\times n\\times (m-1)n$ tensors over the real number field. Let $\\rho$ be the Hurwitz-Radon function defined as $\\rho(n)=2^b+8c$ for nonnegative integers $a,b,c$ such that $n=(2a+1)2^{b+4c}$ and $0\\leq b<4$. If $m \\leq \\rho(n)$, then the set of $m\\times n\\times (m-1)n$ tensors has two typical ranks $(m-1)n,(m-1)n+1$. In this paper, we show that the converse is also true: if $m > \\rho(n)$, then the set of $m\\times n\\times (m-1)n$ tensors has onl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6713","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"}