{"paper":{"title":"A characterization of nonnegativity relative to proper cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chandrashekaran Arumugasamy, Sachindranath Jayaraman, Vatsalkumar N. Mer","submitted_at":"2018-01-30T04:34:46Z","abstract_excerpt":"Let $A$ be an $m \\times n$ matrix with real entries. Given two proper cones $K_1$ and $K_2$ in $\\mathbb{R}^n$ and $\\mathbb{R}^m$, respectively, we say that $A$ is nonnegative if $A(K_1) \\subseteq K_2$. $A$ is said to be semipositive if there exists a $x \\in K_1^\\circ$ such that $Ax \\in K_2^\\circ$. We prove that $A$ is nonnegative if and only if $A+B$ is semipositive for every semipositive matrix $B$. Applications of the above result are also brought out."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09849","kind":"arxiv","version":7},"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"}