符号非奇异的双星符号模式
Sign‑Nonsingular Double‑Star Sign Patterns
DOI: 10.12677/aam.2026.1510426, PDF,   
作者: 沈雨晴：辽宁师范大学数学学院，辽宁 大连
关键词: 符号模式；双星符号模式；符号非奇异；Sign Pattern； Double Star Sign Pattern； Sign‑Nonsingular
摘要: 本文基于双星符号模式的结构特点，研究双星符号模式是否符号非奇异。借助组合矩阵论和图论的理论知识，根据双星符号模式对角线中零元素的数量分情形讨论，给出了n阶双星符号模式符号非奇异的具体结构。该研究结果丰富了树符号模式理论，对符号模式矩阵的相关研究提供了一点新思路，具有一定借鉴意义。
Abstract: This paper investigates whether a double‑star sign pattern is sign‑nonsingular based on its structural characteristics. With the aid of theories from combinatorial matrix theory and graph theory, we discuss different cases according to the number of zero entries on the diagonal of a double‑star sign pattern, and present the concrete structures for an n-order double‑star sign pattern to be sign‑nonsingular. The obtained results enrich the theory of tree sign patterns, offer some new ideas for relevant research on sign pattern matrices, and possess certain reference value.
文章引用：沈雨晴. 符号非奇异的双星符号模式[J]. 应用数学进展, 2026, 15(10): 427-434. https://doi.org/10.12677/aam.2026.1510426

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