{"paper":{"title":"On orthogonal tensors and best rank-one approximation ratio","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AG","math.OC"],"primary_cat":"math.NA","authors_text":"Andr\\'e Uschmajew, Tasuku Soma, Yuji Nakatsukasa, Zhening Li","submitted_at":"2017-07-09T12:06:07Z","abstract_excerpt":"As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an $m \\times n$ matrix with $m \\le n$ is $1/\\sqrt{m}$ and is (up to scalar scaling) attained only by matrices having pairwise orthonormal rows. In the present paper, the smallest possible ratio between spectral and Frobenius norms of $n_1 \\times \\dots \\times n_d$ tensors of order $d$, also called the best rank-one approximation ratio in the literature, is investigated. The exact value is not known for most configurations of $n_1 \\le \\dots \\le n_d$. Using a natural definition of orthogonal tensors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02569","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"}