{"paper":{"title":"Associating vectors in $\\CC^n$ with rank 2 projections in $\\RR^{2n}$: with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Desai Cheng, Peter G. Casazza","submitted_at":"2017-03-08T01:12:30Z","abstract_excerpt":"We will see that vectors in $\\CC^n$ have natural analogs as rank 2 projections in $\\RR^{2n}$ and that this association transfers many vector properties into properties of rank two projections on $\\RR^{2n}$. We believe that this association will answer many open problems in $\\CC^n$ where the corresponding problem in $\\RR^n$ has already been answered - and vice versa. As a application, we will see that phase retrieval (respectively, phase retrieval by projections) in $\\CC^n$ transfers to a variation of phase retrieval by rank 2 projections (respectively, phase retrieval by projections) on $\\RR^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02657","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"}