{"paper":{"title":"A new S-type eigenvalue localization set for tensors and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jingjing Cui, Ligong Wang, Zhengge Huang, Zhong Xu","submitted_at":"2016-02-24T15:46:42Z","abstract_excerpt":"A new \\emph{S}-type eigenvalue localization set for tensors is derived by breaking $N=\\{1,2,\\cdots,n\\}$ into disjoint subsets $S$ and its complement. It is proved that this new set is tighter than those presented by Qi (Journal of Symbolic Computation 40 (2005) 1302-1324), Li et al. (Numer. Linear Algebra Appl. 21 (2014) 39-50) and Li et al. (Linear Algebra Appl. 493 (2016) 469-483). As applications, checkable sufficient conditions for the positive definiteness and the positive semi-definiteness of tensors are proposed. Moreover, based on this new set, we establish a new upper bound for the sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07568","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"}