報告題目：Similarity via transversal intersection of manifolds
報 告 人：李忠善 教授 美國佐治亞州立大學
報告時間：2024年6月29日 15:30-16:30
報告地點：數學樓第2報告廳
校内聯系人：杜現昆 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.
報告人簡介：李忠善，美國佐治亞州立大學數學系終身教授，主要從事矩陣論的研究，包括符号模式矩陣、最小秩問題、非負矩陣、代數圖論、整數矩陣、矩陣方程的有理解、實線性子空間的符号向量集等。李忠善教授目前擔任美國《Mathematical Reviews》特約評論員，《JP Journal of Algebra，Number Theory and Applications》和《Special Matrices》雜志編委等。
