潜在稳定的Hessenberg符号模式
Hessenberg Sign Patterns of Potentially Stable
摘要: 符号模式矩阵(简称符号模式)是组合矩阵论的一个重要研究对象，主要研究与矩阵中元素符号有关而与元素的数值无关的组合性质。针对符号模式的潜在稳定问题，基于Hessenberg矩阵的结构特点，考虑了Hessenberg符号模式。利用正确符号嵌套与潜在稳定之间的联系，给出了3阶潜在稳定的Hessenberg符号模式以及一类特殊的n阶潜在稳定的Hessenberg符号模式。
Abstract: Sign pattern matrices (short for sign patterns) is an important research subject in combinatorial matrix theory, which are related only to signs of their entries and not to the value of entries. Addressing the Potentially Stable problem of sign patterns, this Hessenberg sign patterns based on the structural characteristics of Hessenberg. By the connection between allowing a properly signed nest and Potentially Stable, we investigated 3-order potentially stable Hessenberg sign patterns and a special class of n-order potentially stable Hessenberg sign patterns.
文章引用：谷美璇. 潜在稳定的Hessenberg符号模式[J]. 应用数学进展, 2025, 14(11): 123-127. https://doi.org/10.12677/aam.2025.1411468

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