{"paper":{"title":"Operator scaling with specified marginals","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.CC","math.AG","math.OC","quant-ph"],"primary_cat":"math.CO","authors_text":"Cole Franks","submitted_at":"2018-01-01T22:40:13Z","abstract_excerpt":"The completely positive maps, a generalization of the nonnegative matrices, are a well-studied class of maps from $n\\times n$ matrices to $m\\times m$ matrices. The existence of the operator analogues of doubly stochastic scalings of matrices is equivalent to a multitude of problems in computer science and mathematics, such rational identity testing in non-commuting variables, noncommutative rank of symbolic matrices, and a basic problem in invariant theory (Garg, Gurvits, Oliveira and Wigderson, FOCS, 2016).\n  We study operator scaling with specified marginals, which is the operator analogue o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01412","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"}