报告主题：迫使所有特征根互异的符号模式矩阵
报告人： 李忠善 教授 （Georgia State University）
报告时间：2019年6月14日（周五）10:00
报告地点：校本部G508
邀请人：谭福平
主办部门：理学院数学系
报告摘要：A sign pattern (matrix) is a matrix whose entries are from the set {+, -, 0}. We say that a sign pattern A requires a certain matrix property P if every real matrix whose entries have signs agreeing with A has the property P. Some necessary or sufficient conditions for a square sign pattern to require all distinct eigenvalues are presented. Characterization of such sign pattern matrices is equivalent to determining when a certain real polynomial takes on only positive values whenever all of its variables are assigned arbitrarily chosen positive values. It is known that such sign patterns require a fixed number of real eigenvalues. The $3 \times 3$ irreducible sign patterns that require 3 distinct eigenvalues have been identified previously. We characterize the $4 \times 4$ irreducible sign patterns that require four distinct real eigenvalues and those that require four distinct nonreal eigenvalues. The $4 \times 4$ irreducible sign patterns that require two distinct real eigenvalues and two distinct nonreal eigenvalues are investigated. Some related open problems are discussed.
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