27th Conference of the International Linear Algebra Society (ILAS 2026)

Symmetric nonnegative trifactorization rank of matrices with a given pattern without a four cycle

May 18, 2026, 5:00 PM

25m

Torgersen Hall 1060

Minisymposium Talk Low-rank Matrix and Tensor Decompositions: Theory, Algorithms and Applications Low-rank Matrix and Tensor Decompositions: Theory, Algorithms and Applications

Speaker

Damjana Kokol Bukovšek (University of Ljubljana)

Description

We consider a symmetric nonnegative matrix $A$ of order $n \times n$. A factorization of the form $A = BCB^T$, where $B$ is a nonnegative matrix of order $n \times k$ and $C$ is a symmetric nonnegative matrix of order $k \times k$, is called symmetric nonnegative trifactorization (SNT for short) of $A$. Minimal possible $k$ in such factorization is called the SNT-rank of $A$.

The zero-nonzero pattern of a matrix can be described by a simple graph that allows loops. The SNT-rank of a graph $G$ is the minimal SNT-rank of all symmetric matrices with pattern determined by $G$, and it can be characterized combinatorially using set-join covers of $G$. In the talk we will consider a family of graphs that do not contain four cycles. We will present an algorithm on the graph for computing SNT-rank of such graphs.