On Factorizations of Upper Triangular Nonnegative Matrices of Order Three

Yi-Zhi Chen

doi:10.1155/2015/960182

Abstract

LetT3(N0)denote the semigroup of3×3upper triangular matrices with nonnegative integral-valued entries. In this paper, we investigate factorizations of upper triangular nonnegative matrices of order three. Firstly, we characterize the atoms of the subsemigroupSof the matrices inT3(N0)with nonzero determinant and give some formulas. As a consequence, problems 4a and 4c presented by Baeth et al. (2011) are each half-answered for the casen=3. And then, we consider some factorization cases of matrixAinSwithρ(A)=1and give formulas for the minimum factorization length of some special matrices inS.

Highlights

Introduction and PreliminariesUpper triangular matrices are an important class of matrices, which lead to a broader study of all integral-valued matrices
There are many papers in the literature considering these matrices and similar topics. Factoring such matrices plays a vital role in the study of upper triangular matrices
Problems 4a and 4c presented by Baeth et al in [7] are each half-answered for the case n = 3

Summary

Introduction

Introduction and PreliminariesUpper triangular matrices are an important class of matrices, which lead to a broader study of all integral-valued matrices. We will investigate factorizations of upper triangular nonnegative matrices of order three.

Results

Conclusion