Minimal critical sets of refined inertias for irreducible sign patterns of order 3
Minimal critical sets of refined inertias for irreducible sign patterns of order 3
投稿时间:2019-01-25  修订日期:2019-11-14
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英文关键词:Sign pattern  Refined inertia  Refined inertially arbitrary sign pattern  Critical
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作者单位E-mail
王娅静 中北大学大数据学院 s1408028@st.nuc.edu.cn 
高玉斌 中北大学理学院 ybgao@nuc.edu.cn 
邵燕灵 中北大学理学院  
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      Let S be a nonempty, proper subset of all possible refined inertias of real matrices of order n. The set S is a critical set of refined inertias for irreducible sign patterns of order n, if for each n×n irreducible sign pattern A, the condition S ? ri(A) is sufficient for A to be refined inertially arbitrary. If no proper subset of S is a critical set of refined inertias, then S is a minimal critical set of refined inertias for irreducible sign patterns of order n. All minimal critical sets of refined inertias for full sign patterns of order 3 have been identified [Wei GAO, Zhongshan LI, Lihua ZHANG, The minimal critical sets of refined inertias for 3 × 3 full sign patterns, Linear Algebra Appl. 458(2014), 183–196]. In this paper, the minimal critical sets of refined inertias for irreducible sign patterns of order 3 are identified.
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