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  • Symmetric nonnegative trifactorization of pattern matrices
    Kokol-Bukovšek, Damjana ; Šmigoc, Helena
    A factorization of an n x n nonnegative symmetric matrix A of the form BCBT, where C is a k x k symmetric matrix, and both B and C are required to be nonnegative, is called the Symmetric Nonnegative ... Matrix Trifactorization (SN-Trifactorization). The SNT-rank of A is the minimal k for which such factorization exists. The SNT-rank of a simple graph G that allows loops is defined to be the minimal possible SNT-rank of all symmetric nonnegative matrices whose zero-nonzero pattern is prescribed by the graph G. We define set-join covers of graphs, and show that finding the SNT-rank of G is equivalent to finding the minimal order of a set-join cover of G. Using this insight we develop basic properties of the SNT-rank for graphs and compute it for trees and cycles without loops. We show the equivalence between the SNT-rank for complete graphs and the Katona problem, and discuss uniqueness of patterns of matrices in the factorization.
    Vir: Linear algebra and its applications. - ISSN 0024-3795 ([in press] 2024)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2024
    Jezik - angleški
    COBISS.SI-ID - 197444611
    DOI

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