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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.4966","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-01-20T16:17:19Z","cross_cats_sorted":[],"title_canon_sha256":"38baa7737e8e308e3ff5a96971e19e350a3f207649c63a317d877449af4f4310","abstract_canon_sha256":"cfb66df978d689c85a62910919ae0bb5d4dc84b1932954c7e953880a7935caba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:34.951615Z","signature_b64":"3hRXABdOeDOXvc6lRonfwIGR0DYLARcQGCeZxK+JYPRQgSJv5pvceatGe+XmtZR0VuVP9NBRKz95yyXhTZjPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd533650a9be3f6ef88aaf26bdff7376912ec43f9c140ef06707de51151ac985","last_reissued_at":"2026-05-18T03:01:34.951154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:34.951154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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