摘要
设A,B∈Cn×n为广义二次矩阵,C∈Cn×n,并定义广义Jordan积为AC+CB.应用广义二次矩阵和幂等矩阵的互为确定的关系,得到了由两个不同的幂等矩阵确定的广义二次矩阵A和B与任意矩阵C的广义Jordan积的秩不变性.该结果改进了已有二次矩阵的相关结果.
AC+CBis called as the generalized Jordan product of generalized quadratic matricesAandB,for anyC∈C^(n×n).By applying mutual determination relationship between generalized quadratic matrix and idempotent matrix,we obtained invariance of rank for generalized Jordan products of generalized quadratic matrcesA,Band any complex matrixC,in whichA,Bare determined by two different idempotent matrices.The results improve the relevant results of quadratic matrices.
作者
吕洪斌
陈梅香
杨忠鹏
冯晓霞
LÜHongbin;CHEN Meixiang;YANG Zhongpeng;FENG Xiaoxia(School of Mathematics and Statistics,Beihua University,Jilin 132013,China;School of Mathematics and Finance,Putian University,Putian 351100,China;School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)
出处
《延边大学学报（自然科学版）》
CAS
2021年第4期289-296,共8页
Journal of Yanbian University（Natural Science Edition）
基金
吉林省科技发展计划项目(20190201139JC)
福建省自然科学基金(2021J011103)。
关键词
二次矩阵
广义二次矩阵
秩
广义Jordan积
不变性
quadratic matrix
generalized quadratic matrix
rank
generalized Jordan product
invariance
