模式矩阵的对称非负三因子化

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-05-28 DOI:10.1016/j.laa.2024.05.017

Damjana Kokol Bukovšek, Helena Šmigoc

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引用次数: 0

摘要

一个非负对称矩阵的因式分解形式为，其中，是一个对称矩阵，且和都必须是非负矩阵，这种因式分解称为对称非负矩阵三因式分解（SN-Trifactorization）。的 SNT-rank 是存在这种因式分解的最小值。允许循环的简单图的 SNT-rank 定义为所有对称非负矩阵的最小可能 SNT-rank，这些矩阵的零-非零模式由图规定。

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Symmetric nonnegative trifactorization of pattern matrices

A factorization of an nonnegative symmetric matrix of the form , where is a symmetric matrix, and both and are required to be nonnegative, is called the Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization). The SNT-rank of is the minimal for which such factorization exists. The SNT-rank of a simple graph 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 .

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.