华罗庚的矩阵情结与矩阵“打洞”技术的应用  

Hua Loo-Keng’s Matrix Complex and Applications of“Hole Drilling”Technology

作　　者：晏瑜敏[1,2] 刘艳芳 杨忠鹏[1,2] 林志兴[1,2] 陈智雄[1,2] 陈梅香[1,2] YAN Yumin;LIU Yanfang;YANG Zhongpeng;LIN Zhixing;CHEN Zhixiong;CHEN Meixiang(Key Laboratory of Applied Mathematics of Fujian Province University(Putian University),Putian 351100,China;Key Laboratory of Financial Mathematics of Fujian Province University(Putian University),Putian 351100,China;College of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]应用数学福建省高校重点实验室(莆田学院),福建莆田351100 [2]金融数学福建省高校重点实验室(莆田学院),福建莆田351100 [3]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《北华大学学报（自然科学版）》2023年第2期141-149,共9页Journal of Beihua University（Natural Science）

基　　金：国家自然科学基金项目(61772292);福建省自然科学基金项目(2021J011103,2021J05238);莆田市科技局项目(2022SZ3001ptxy05);福建省教育改革项目(FBJG20210174);莆田学院教改项目(JG2022053)。

摘　　要：在回顾华罗庚的数学研究与其一生的矩阵情结的关系的基础上,重点探讨了极具中国传统文化特色的矩阵打洞技术对矩阵理论研究与教学的深刻影响.注意到矩阵打洞技术在近年来考研试题的广泛应用,指出“打洞”的反向——“补洞”技术是解决一些难题的强有力工具.将打洞与补洞有机结合,对全面理解运用华罗庚学派的矩阵理论及应用是很有意义的.On the basis of reviewing the relationship between Hua Loo-Keng’s mathematical research and strong complex of matrix,this paper focuses on the profound influence of matrix hole drilling technology with Chinese traditional culture characteristics on the research and teaching of matrix theory.With the wide use of matrix holedrilling technology in the postgraduate entrance examination questions in recent years,the reverse“Hole Filling”technology of“Hole Drilling”is pointed out to solve some difficult problems.Combining the“Hole Drilling”and“Hole Filling”technology organically will be significant to understand and apply the matrix theory of Hua system.

关 键 词：华罗庚 矩阵 矩阵打洞 矩阵补洞 分块初等变换 

分 类 号：O151.21[理学—数学]