L Hongbin,CHEN Meixiang,YANG Zhongpeng,et al.Invariance of rank for generalized Jordan products of generalized quadratic matrices[J].Journal of Yanbian University,2021,47(04):289-296.
与广义二次矩阵相关的广义Jordan积秩的不变性
- Title:
- Invariance of rank for generalized Jordan products of generalized quadratic matrices
- 文章编号:
- 1004-4353(2021)04-0289-08
- Keywords:
- quadratic matrix; generalized quadratic matrix; rank; generalized Jordan product; invariance
- 分类号:
- O151.21
- 文献标志码:
- A
- 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.
- Abstract:
- AC+CB is called as the generalized Jordan product of generalized quadratic matrices A and B, for any C∈Cn ×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 matrces A,B and any complex matrix C, in which A,B are determined by two different idempotent matrices.The results improve the relevant results of quadratic matrices.
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备注/Memo
收稿日期: 2021-09-07
基金项目: 吉林省科技发展计划项目(20190201139JC); 福建省自然科学基金(2021J011103)
第一作者: 吕洪斌(1964—),男,博士,教授,研究方向为数值代数、矩阵理论及其应用.
通信作者: 杨忠鹏(1947—),男,学士,教授,研究方向为矩阵理论及其应用.