3阶零对角组合对称符号模式矩阵

Zero Diagonal Combinatorial Symmetric Sign Pattern Matrices with Order 3

本文基于组合对称符号模式矩阵的结构特点,考虑了零对角组合对称符号模式矩阵,讨论了3阶零对角组合对称符号模式矩阵是否允许代数正以及要求代数正。利用组合矩阵论和图论的理论,借助Maple软件,通过特征值的方法,分别给出了3阶零对角组合对称符号模式矩阵是允许代数正以及要求代数正的等价条件,从而确定了允许代数正的3阶零对角组合对称符号模式矩阵和要求代数正的3阶零对角组合对称符号模式矩阵的具体结构。

Based on the structural characteristics of the combinatorial symmetric matrix, the zero diagonal combinatorial symmetric sign pattern matrices are considered, and whether the zero diagonal combinatorial symmetric sign pattern matrices with order 3 allow algebraic positivity and require algebraic positivity are discussed. By using the theory of combinatorial matrix theory and graph theory, with the help of Maple software and the method of eigenvalues, this paper gives the equiva-lent conditions that the zero diagonal combinatorial symmetric sign pattern matrices allow alge-braic positivity and require algebraic positivity, respectively, thus determines the specific struc-tures of the zero diagonal combinatorial symmetric sign pattern matrices with order 3 that allow algebra positive and the zero diagonal combinatorial symmetric sign pattern matrices with order 3 that require algebraic positivity.