{"paper":{"title":"Infinite and finite dimensional Hilbert tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Liqun Qi, Yisheng Song","submitted_at":"2014-01-20T16:17:19Z","abstract_excerpt":"For an $m$-order $n-$dimensional Hilbert tensor (hypermatrix) $\\mathcal{H}_n=(\\mathcal{H}_{i_1i_2\\cdots i_m})$, $$\\mathcal{H}_{i_1i_2\\cdots i_m}=\\frac1{i_1+i_2+\\cdots+i_m-m+1},\\ i_1,\\cdots, i_m=1,2,\\cdots,n$$ its spectral radius is not larger than $n^{m-1}\\sin\\frac{\\pi}{n}$, and an upper bound of its $E$-spectral radius is $n^{\\frac{m}2}\\sin\\frac{\\pi}{n}$. Moreover, its spectral radius is strictly increasing and its $E$-spectral radius is nondecreasing with respect to the dimension $n$. When the order is even, both infinite and finite dimensional Hilbert tensors are positive definite. We also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4966","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"}