Toeplitz符号模式矩阵的一些研究  

Some Studies on Toeplitz Sign Pattern Matrices

作　　者：赵心茹 田岩 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2023年第1期332-338,共7页Advances in Applied Mathematics

摘　　要：本文主要考虑Toeplitz符号模式矩阵,研究3阶Toeplitz符号模式矩阵是否允许代数正。结合组合矩阵论和图论的理论,研究零对角的3阶Toeplitz符号模式矩阵,给出零对角的3阶Toeplitz符号模式矩阵允许代数正的等价条件。同时,给出一类允许代数正的3阶Toeplitz符号模式矩阵及其具体结构。This paper mainly considers Toeplitz sign pattern matrices, whether Toeplitz sign pattern matrices with order 3 allow algebraic positivity is studied. Combining the theories of combinatorial matrix theory and graph theory, zero diagonal Toeplitz sign pattern matrices with order 3 were studied, the equivalent conditions of the zero diagonal Toeplitz sign pattern matrices with order 3 that allow algebraic positivity were given. At the same time, a class of Toeplitz sign pattern matrices with or-der 3 that allow algebraic positivity and their specific structure were given.

关 键 词：符号模式矩阵 Toeplitz符号模式矩阵 允许代数正 

分 类 号：O15[理学—数学]