报告题目：Similarity via transversal intersection of manifolds
报 告 人：李忠善 教授 美国佐治亚州立大学
报告时间：2024年6月29日 15:30-16:30
报告地点：数学楼第2报告厅
校内联系人：杜现昆 duxk@jlu.edu.cn
摘要: In this talk, transversality property of an n by n real matrix A is characterized using the similarity-transversality property (STP). This new approach makes it possible to take better advantage of the combinatorial structure of the matrix A, and provides theoretical foundation for constructing matrices similar to a given matrix while the entries have certain desired signs. In particular, important classes of zero-nonzero patterns and sign patterns that require or allow this transversality property are identified. Examples illustrating many possible applications (such as diagonalizability, number of distinct eigenvalues, nilpotence, idempotence, semi-stability, the minimal polynomial, and rank) are provided. Several intriguing open problems are raised.
报告人简介：李忠善，美国佐治亚州立大学数学系终身教授，主要从事矩阵论的研究，包括符号模式矩阵、最小秩问题、非负矩阵、代数图论、整数矩阵、矩阵方程的有理解、实线性子空间的符号向量集等。李忠善教授目前担任美国《Mathematical Reviews》特约评论员，《JP Journal of Algebra，Number Theory and Applications》和《Special Matrices》杂志编委等。
