{"paper":{"title":"On the similarity of Tensors","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lihua You, Pingzhi Yuan","submitted_at":"2013-09-20T07:11:32Z","abstract_excerpt":"Let $\\mathbb{P}_n$ be the set of all matrices which have the same zero patterns with some permutation matrix of order $n$.\n  In this paper, we prove the following result: Let $\\mathbb{I}$ be the unit tensor of order $m\\ge3$ and dimension $n\\ge2$. Suppose that $P$ and $Q$ are two matrices with $P\\mathbb{I}Q=\\mathbb{I}$, then $P,Q\\in \\mathbb{P}_n$. This gives a characterization for the similarities of tensors with order $m\\ge3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5189","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"}