Toeplitz符号模式矩阵的一些研究
Some Studies on Toeplitz Sign Pattern Matrices
DOI: 10.12677/AAM.2023.121036, PDF,    科研立项经费支持
作者: 赵心茹, 田 岩*：辽宁师范大学数学学院，辽宁 大连
关键词: 符号模式矩阵；Toeplitz符号模式矩阵；允许代数正；Sign Pattern Matrix； Toeplitz Sign Pattern Matrix； Allow Algebraic Positivity
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。
Abstract: 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.
文章引用：赵心茹, 田岩. Toeplitz符号模式矩阵的一些研究[J]. 应用数学进展, 2023, 12(1): 332-338. https://doi.org/10.12677/AAM.2023.121036

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