代数正矩阵的若干研究  

Some studies on algebraic positive matrices

作　　者：田岩 焦旸 TIAN Yan;JIAO Yang(School of Mathematics, Liaoning Normal University, Dalian 116029, China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2022年第2期152-158,共7页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学研究青年项目(LQ2020021)。

摘　　要：符号模式矩阵是组合矩阵论的一个新兴研究热点,它在经济学、生物学、化学、社会学、计算机科学等众多学科中有广泛应用.符号模式主要研究仅与矩阵元素的符号有关的组合性质.然而,符号模式矩阵要求代数正和允许代数正仍然是两个重要的公开问题.本文首先通过对代数正矩阵的研究,给出代数正矩阵的一些性质,然后将实矩阵进行约化.最后,利用代数正矩阵的性质,研究3阶不可约的三对角符号模式矩阵,给出3阶不可约的三对角符号模式矩阵是允许代数正的一个等价刻画.The sign pattern matrix is a new research hotspot of combinatorial matrix theory.It is widely used in economics,biology,chemistry,sociology,computer science and many other disciplines.Sign pattern matrices mainly study the combinatorial properties related only to the symbols of the elements of a matrix.However,sign pattern matrices require algebraic positivity and allow algebraic positivity are still two important open problems.In this paper,we give some properties of algebraic positive matrices through the study of algebraic positive matrices,and then reduce the real matrices.Finally,we study all irreducible tridiagonal sign pattern matrices of order 3 by virtue of the properties of algebraic positive matrices.We also give an equivalent characterization of irreducible tridiagonal sign pattern matrices of order 3 that allow algebraic positivity.

关 键 词：代数正 符号模式矩阵 允许代数正 

分 类 号：O151.21[理学—数学]