2026/07/29 by Bharat Pratap Chauhan, Projesh Nath Choudhury
Mathematics · #math.RA
15 pages, no figures
arxiv created 2026/07/29 · arxiv updated 2026/07/30
Symmetric nonnegative matrix trifactorizations (SN-Trifactorizations) were introduced by Bukovšek-Šmigoc [Linear Algebra Appl. 2023] as a symmetric analogue of nonnegative matrix factorizations. A SN-Trifactorization of a symmetric nonnegative matrix A is of the form A = BCBT, where B and C are nonnegative matrices, with C symmetric. The associated SNT-rank of A is defined as the smallest integer k for which A admits such a factorization with C ∈ ℝ+k × k. In this paper, we derive sharper upper bounds for the SNT-rank of the Euclidean distance matrices considered by Shitov [Linear Algebra Appl. 2025] and Bukovšek-Šmigoc [Linear Algebra Appl. 2023]. We also establish several new relationships between the rank and the SNT-rank of symmetric nonnegative matrices and show that the SNT-rank is submultiplicative with respect to the Kronecker product. Finally, motivated by a conjecture posed in the Dagstuhl Seminar Report 13082, we prove a multiplicativity result for the nonnegative rank under an additional structural assumption. We also partially resolve a conjecture of Vandaele-Gillis-Glineur-Tuyttens [J. Global Optim. 2016].