{"paper":{"title":"Rank of tensors with size 2 x ... x 2","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":"2013-06-04T09:14:52Z","abstract_excerpt":"We study an upper bound of ranks of $n$-tensors with size $2\\times\\cdots\\times2$ over the complex and real number field. We characterize a $2\\times 2\\times 2$ tensor with rank 3 by using the Cayley's hyperdeterminant and some function. Then we see another proof of Brylinski's result that the maximal rank of $2\\times2\\times2\\times2$ complex tensors is 4. We state supporting evidence of the claim that 5 is a typical rank of $2\\times2\\times2\\times2$ real tensors. Recall that Kong and Jiang show that the maximal rank of $2\\times2\\times2\\times2$ real tensors is less than or equal to 5. The maximal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0708","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"}