爪型符号模式矩阵要求代数正的相关研究

Related research on paw form sign pattern matrices that require algebraic positivity

基于爪形符号模式矩阵的结构特点,研究了爪型符号模式矩阵是否要求代数正.利用图论和组合矩阵论的知识,证明了爪型符号模式矩阵要求代数正的必要条件.同时,分别给出了阶数小于5的爪型符号模式矩阵要求代数正的等价条件.研究结论丰富了组合矩阵理论,为符号模式矩阵允许代数正和要求代数正的研究提供了方法和思路.

Based on the structural characteristics of paw form sign pattern matrices,whether the paw form sign pattern matrices require algebraic positivity are studied in this paper.It is proved that the necessary condi-tions of the paw form sign pattern matrices that require algebraic positivity by using the knowledge of graph theory and combinatorial matrix theory.At the same time,some equivalent conditions of the paw form sign pattern matrices with order less than 5 that require algebraic positivity are given respectively.The results of this paper enriches the combinatorial matrix theory,the methods and ideas are provided for the study of allowing algebraic positivity and requiring algebraic positivity of sign pattern matrices.