Hurwitz-Radon矩阵方程的华罗庚链  

Hua’s Cyclic Recurrence Relation for Hurwitz-Radon Matrix Equations

作　　者：林开亮[1] 赵教练 LIN Kailiang;ZHAO Jiaolian(College of Science,Northwest Agricultural and Forestry University,Yangling 712100,China;School of Mathematics and Statistics,Weinan Normal University,Weinan 714099,China)

机构地区：[1]西北农林科技大学理学院,陕西杨凌712100 [2]渭南师范学院数学与统计学院,陕西渭南714099

出　　处：《渭南师范学院学报》2023年第2期75-84,共10页Journal of Weinan Normal University

基　　金：国家自然科学基金数学天元基金项目:华罗庚及其学派的研究和普及(1182601057)。

摘　　要：1947年,华罗庚独立研究了Hurwitz-Radon矩阵方程,遗憾的是由于失误他未能得出完整结果。文章补充完善了华罗庚对于Hurwitz-Radon矩阵方程的求解。遵循华罗庚的思路,所采用的方法是矩阵的相似标准型。得到了华罗庚链,并通过酉化技巧得到其酉版本。Loo Keng Hua studied Hurwitz-Radon matrix equations independently in 1947.However,Hua didn’t get the full results due to some mistakes.The present paper completes Hua’s original solution for Hurwitz-Radon matrix equations.Following Hua,the method is based on the canonical forms of matrices under similarity transforms.Hua’s cyclic recurrence relation and its unitary version are presented.

关 键 词：Hurwitz-Radon矩阵方程 Hurwitz-Radon定理 华罗庚链 酉化技巧 矩阵标准型 

分 类 号：O15[理学—数学]