Eigenvalue continuity and a few issues in teaching linear algebra

主讲人：张福振 美国诺瓦东南大学教授

时间：2024年6月14日13：30

地点：三号楼332室

举办单位：数理学院

主讲人介绍：张福振，现为美国Nova Southeastern University（诺瓦东南大学）数学系教授。主要研究线性与多重线性代数及矩阵分析、算子理论、泛函分析和组合数学。至今发表学术论文80余篇，著作3部。曾任美国数学会《数学评论》 评审人,国际线性代数学会公报《IMAGE》编委,美国自然科学基金评委。现任多家国际数学杂志编委或客座编委。若干国际数学专业会议主讲人,其中包括第18届国际线性代数学会大会，第22届国际矩阵与统计研讨班，和田纳西大学线性代数及图论会。国际矩阵分析及应用系列会议组委会主席。第19届国际线性代数学会大会组委会成员。在世界各地专业会议中报告80余次。近年来在中国一些高校就中美高等教育演讲。被聘为上海大学等高校兼职教授。参与创建佛州华人华侨联合会，并曾任主席(1994-1996)，南佛州现代中文学校校长等职。2013年获诺瓦东南大学文理学院杰出教授奖。

内容介绍：Are eigenvalues continuous functions of matrix entries? In other words, do the eigenvalues of a matrix change continuously as the matrix itself undergoes small changes? (The answer is yes or no, depending on what is meant by eigenvalue continuity). Eigenvalue continuity is a fundamental concept in linear algebra and matrix theory that provides insights into the behavior of eigenvalues under small changes to matrices, with wide-ranging implications in theory and applications. However, eigenvalue continuity has been misused or carelessly used. We discuss the continuity of eigenvalues as functions (functional continuity) as well as in the topological sense (topological continuity). This talk is also concerned with a few issues of linear algebra, both in teaching and research. These issues are usually overlooked or carelessly treated in texts or teaching.