Minimal Critical Sets of Refined Inertias for Irreducible Sign Patterns of Order 3  

作　　者：Yajing WANG Yubin GAO Yanling SHAO 

机构地区：[1]Department of Data Science and Technology,North University of China,Shanxi 030051,P.R.China [2]Department of Mathematics,North University of China,Shanxi 030051,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2020年第3期246-262,共17页数学研究及应用（英文版）

基　　金：Supported by Shanxi Province Science Foundation for Youths(Grant No.201901D211227).

摘　　要：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 in [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.

关 键 词：sign pattern refined inertia refined inertially arbitrary sign pattern critical set of refined inertias 

分 类 号：O144[理学—数学]