{"paper":{"title":"Finsler's Lemma for Matrix Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jaka Cimpric","submitted_at":"2014-06-28T21:27:43Z","abstract_excerpt":"Finsler's Lemma charactrizes all pairs of symmetric $n \\times n$ real matrices $A$ and $B$ which satisfy the property that $v^T A v>0$ for every nonzero $v \\in \\mathbb{R}^n$ such that $v^T B v=0$. We extend this characterization to all symmetric matrices of real multivariate polynomials, but we need an additional assumption that $B$ is negative semidefinite outside some ball. We also give two applications of this result to Noncommutative Real Algebraic Geometry which for $n=1$ reduce to the usual characterizations of positive polynomials on varieties and on compact sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7442","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"}