Eigenvalue continuity and a few issues in teaching linear algebra

主講人：張福振 美國諾瓦東南大學(xué)教授

時間：2024年6月14日13：30

地點：三號樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：張福振，現(xiàn)為美國Nova Southeastern University（諾瓦東南大學(xué)）數(shù)學(xué)系教授。主要研究線性與多重線性代數(shù)及矩陣分析、算子理論、泛函分析和組合數(shù)學(xué)。至今發(fā)表學(xué)術(shù)論文80余篇，著作3部。曾任美國數(shù)學(xué)會《數(shù)學(xué)評論》 評審人,國際線性代數(shù)學(xué)會公報《IMAGE》編委,美國自然科學(xué)基金評委?，F(xiàn)任多家國際數(shù)學(xué)雜志編委或客座編委。若干國際數(shù)學(xué)專業(yè)會議主講人,其中包括第18屆國際線性代數(shù)學(xué)會大會，第22屆國際矩陣與統(tǒng)計研討班，和田納西大學(xué)線性代數(shù)及圖論會。國際矩陣分析及應(yīng)用系列會議組委會主席。第19屆國際線性代數(shù)學(xué)會大會組委會成員。在世界各地專業(yè)會議中報告80余次。近年來在中國一些高校就中美高等教育演講。被聘為上海大學(xué)等高校兼職教授。參與創(chuàng)建佛州華人華僑聯(lián)合會，并曾任主席(1994-1996)，南佛州現(xiàn)代中文學(xué)校校長等職。2013年獲諾瓦東南大學(xué)文理學(xué)院杰出教授獎。

內(nèi)容介紹：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.