关于矩阵和的秩等式  

Rank Equality of the Sum of Some Matrices

作　　者：陈佳宏 CHEN Jiahong(School of Mathematics and Statistics, Kashi University, Kashi Xinjiang 844006, Chin)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844006

出　　处：《长沙大学学报》2016年第5期1-4,共4页Journal of Changsha University

基　　金：喀什大学校内青年专项课题(项目编号:(15)2568)

摘　　要：用矩阵打洞的方法给出了有限个矩阵和的秩等式成立等价于这些矩阵可以同时相抵对角化.此结论是对一些文献中已有结论的进一步细化.作为应用,对一些文献中的结论进行了简洁、直接的证明.In this paper,we prove that the condition of establishment of the rank equality about the sum of some matrices is equivalent to the simultaneous diagonalization of these matrices to the rank normal forms by using the method of digging holes in matrices. The main theorems of this paper can be considered as a refinement of some known results. As applications of the main theorems,we provide some concise and straightforward poofs of the results from some references.

关 键 词：秩 矩阵打洞 秩等式 同时对角化 

分 类 号：O151.21[理学—数学]