Symmetric nonnegative matrix trifactorization

Kokol-Bukovšek, Damjana (author), Šmigoc, Helena (author)

The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of an nonnegative symmetric matrix A of the form , where C is a symmetric matrix, and both B and C are required to be nonnegative. This work introduces the SNT-rank of A, as the minimal k, for which such factorization exists. After a list of basic properties and an exploration of SNT-rank of low rank matrices, the class of nonnegative symmetric matrices with SNT-rank equal to rank is studied. The paper concludes with a completion problem, that asks for matrices with the smallest possible SNT-rank among all nonnegative symmetric matrices with given diagonal blocks.

• Language: English
• Keywords: mathematics, mathematical economy, matrix algebra, nonnegative matrix factorization, completely positive matrices, nonnegative symmetric matrices, nonnegative rank
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: EF - School of Economics and Business
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 36-60
• Numbering: Vol. 665
• PID: 20.500.12556/RUL-147833
• UDC: 330.4
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2023.01.027
• COBISS.SI-ID: 140740867
• Publication date in RUL: 13.07.2023

Record is a part of a journal

• Title: Linear algebra and its applications
• Shortened title: Linear algebra appl.
• Publisher: Elsevier
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: matematika, matematična ekonomija, matrična algebra

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika