题目：4×4 Irreducible Sign Pattern Matrices that Require Four Distinct Eigenvalues

报告人：李忠善 教授 （佐治亚州立大学）

地点：致远楼101室

时间：2024年6月20日 星期四 上午10:00-11:30

报告摘要：JP J. Algebra Number Theory Appl., 2:2 (2002), 161--179, Li and Harris characterized the 2×2 and 3×3 irreducible sign pattern matrices that require all distinct eigenvalues, and established some useful general results on n×n sign patterns that require all distinct eigenvalues. In this talk, we characterize 4×4 irreducible sign patterns that require four distinct eigenvalues. This is done by characterizing 4×4 irreducible sign patterns that require four distinct real eigenvalues, that require four distinct nonreal real eigenvalues, or that require two distinct real eigenvalues and a pair of conjugate nonreal eigenvalues. The last case turns out to be much more involved. Some interesting open problems are presented.

报告人简介：李忠善(Zhongshan Li)教授，现为美国Georgia State University（佐治亚州立大学）数学系终身正教授。研究方向包括组合矩阵理论、代数图论、矩阵理论应用等。

先后在《American Mathematical Monthly》，《Linear Algebra and Its Applications》，《SIAM J. on Discrete Mathematics》，《J. Combin. Theory Ser. B》，《Linear and Multilinear Algebra》， 《Graphs and Combinatorics》，《IEEE Transactions on Neural Networks and Learning Systems》 等重要国际学术期刊上发表论文80余篇。李忠善教授目前主要从事组合矩阵论的研究，包括符号模式矩阵、最小秩问题、特征值问题、矩阵流形、代数图论、整数矩阵、实线性子空间的符号向量集等。 李忠善教授目前还担任美国《Mathematical Reviews》特约评论员，《JP Journal of Algebra，Number Theory and Applications》和《Special Matrices》杂志编委等职务。

欢迎各位参加！