{"paper":{"title":"The E-Eigenvectors of Tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Liqun Qi, Shenglong Hu","submitted_at":"2013-03-12T11:12:53Z","abstract_excerpt":"We first show that the eigenvector of a tensor is well-defined. The differences between the eigenvectors of a tensor and its E-eigenvectors are the eigenvectors on the nonsingular projective variety $\\mathbb S=\\{\\mathbf x\\in\\mathbb P^n\\;|\\;\\sum\\limits_{i=0}^nx_i^2=0\\}$. We show that a generic tensor has no eigenvectors on $\\mathbb S$. Actually, we show that a generic tensor has no eigenvectors on a proper nonsingular projective variety in $\\mathbb P^n$. By these facts, we show that the coefficients of the E-characteristic polynomial are algebraically dependent. Actually, a certain power of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2840","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"}