{"paper":{"title":"The Hermitian null-range of a matrix over a finite field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"E. Ballico","submitted_at":"2016-11-27T13:33:45Z","abstract_excerpt":"Let $q$ be a prime power. For $u=(u_1,\\dots ,u_n), v=(v_1,\\dots ,v_n)\\in \\mathbb {F}_{q^2}^n$ let $\\langle u,v\\rangle := \\sum _{i=1}^{n} u_i^qv_i$ be the Hermitian form of $\\mathbb {F} _{q^2}^n$. Fix an $n\\times n$ matrix $M$ over $\\mathbb {F} _{q^2}$. We study the case $k=0$ of the set $\\mathrm{Num} _k(M):= \\{\\langle u,Mu\\rangle \\mid u\\in \\mathbb {F} _{q^2}, \\langle u,u\\rangle =k\\}$. When $M$ has coefficients in $\\mathbb {F} _q$ we study the set $\\mathrm{Num} _0(M)_q:= \\{\\langle u,Mu\\rangle \\mid u\\in \\mathbb {F} _q^n\\}\\subseteq \\mathbb {F} _q$. The set $\\mathrm{Num} _1(M)$ is the numerical ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08840","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"}