{"paper":{"title":"Sinkhorn-Knopp theorem for rectangular positive maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Daniel Cariello","submitted_at":"2016-09-22T17:41:26Z","abstract_excerpt":"In this work, we adapt Sinkhorn-Knopp theorem for rectangular positive maps $(T:M_k\\rightarrow M_m)$. We extend their concepts of support and total support to these maps. We show that a positive map $T:M_k\\rightarrow M_m$ is equivalent to a doubly stochastic map if and only if $T:M_k\\rightarrow M_m$ is equivalent to a positive map with total support.\n  Moreover, if $k$ and $m$ are coprime then $T:M_k\\rightarrow M_m$ is equivalent to a doubly stochastic map if and only if $T:M_k\\rightarrow M_m$ has support.\n  This result provides a necessary and sufficient condition for the filter normal form, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07083","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"}