关于若干个矩阵和的秩等式与不等式  

About rank equalities and inequalities of the sum of some matrices

作　　者：左可正[1] 

机构地区：[1]湖北师范学院数学与统计学院,湖北黄石435002

出　　处：《湖北师范学院学报（自然科学版）》2010年第1期1-4,共4页Journal of Hubei Normal University(Natural Science)

摘　　要：利用维数公式及分块矩阵的秩与矩阵的广义逆的关系,得出了两个关于若干个矩阵和的秩不等式,并给出了这些不等式取等号的一些充要条件。这些结果将两个矩阵和的秩不等式推广到了多个矩阵的秩不等式。By using the dimension formular and the relation between the rank of a block matrix with the generalised inverse of a matrix,two rank inequalities about the sum of some matrices are obtained,and some necessary and sufficient conditions of equate extablishment are given.The rank inequality of the sum of two matrices is seneralized into the case of the sum of several matrices.

关 键 词：广义逆 矩阵的秩 维数公式 

分 类 号：O151.21[理学—数学]