Nonnegative rank depends on the field

• 成果类型: Article
• 署名作者: Shitov, Yaroslav
• 署名单位: Moscow Institute of Physics & Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01448-2
• 发表日期: 2021
• 页码: 479-486
• 关键词: matrix factorization

摘要

We present an example of a subfield F. R and a matrix A whose conventional and nonnegative ranks equal five, but the nonnegative rank with respect to F equals six. In other words, A can be represented as a sum of five rank-one matrices with nonnegative real entries but not as a sum of five rank-one matrices with nonnegative entries in F.