Minimal critical sets of refined inertias for irreducible sign patterns of order 3
Received:January 25, 2019  Revised:November 14, 2019
Key Word: Sign pattern   Refined inertia   Refined inertially arbitrary sign pattern   Critical  
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Author NameAffiliationE-mail
Ya-Jing Wang Data science and technology in north university of china s1408028@st.nuc.edu.cn 
Yu-Bin Gao Department of Mathematic, North University of China ybgao@nuc.edu.cn 
Yan-Ling Shao Department of Mathematic, North University of China  
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Abstract:
      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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