{"paper":{"title":"On the Grassmann condition number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Javier Pena, Vera Roshchina","submitted_at":"2016-04-15T20:38:47Z","abstract_excerpt":"We give new insight into the Grassmann condition of the conic feasibility problem \\[ x \\in L \\cap K \\setminus\\{0\\}. \\] Here $K\\subseteq V$ is a regular convex cone and $L\\subseteq V$ is a linear subspace of the finite dimensional Euclidean vector space $V$. The Grassmann condition of this problem is the reciprocal of the distance from $L$ to the set of ill-posed instances in the Grassmann manifold where $L$ lives.\n  We consider a very general distance in the Grassmann manifold defined by two possibly different norms in $V$. We establish the equivalence between the Grassmann distance to ill-pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04637","kind":"arxiv","version":2},"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"}