|| Unsigned Matrix Completion
||Yunzhen Yao, Liangzu Peng, Manolis C. Tsakiris, ShanghaiTech University, China|
||D5-S4-T3: Topics in Recovery I
||Friday, 16 July, 23:00 - 23:20
||Friday, 16 July, 23:20 - 23:40
Inspired by real phase retrieval and low-rank matrix recovery, we introduce the problem of unsigned matrix retrieval, where the aim is to recover a matrix of bounded-rank from a sign-ambiguous version of it. Allowing for missing entries in addition to sign ambiguities leads to the problem of unsigned matrix completion. Under an algebraic geometry framework, we provide fundamental results regarding unique recovery up to a class of rank-preserving sign patterns and finite completability.