伴随阵与两种广义逆阵的若干性质  

Several Properties of Adjoint Matrix and Two Classes Generalized Inverse Matrices

作　　者：黄敬频[1] 

机构地区：[1]广西民族学院数学与计算机科学系,广西南宁530006

出　　处：《广西民族学院学报（自然科学版）》2002年第4期4-6,共3页Journal of Guangxi University For Nationalities(Natural Science Edition)

基　　金：广西民族学院科研资助项目(02SJX00008).

摘　　要：设adjA,A+,AD分别表示复方阵A的伴随阵、Moore-Penrose逆和Drazin逆.利用矩阵的奇异值分解、约当分解和极限过程的方法,证明了:(adjA)+=adj(A+),(adjA)D=adj(AD);并得到当A是复亚半正定阵时,A+和AD也均为复亚半正定阵,且A+=AD.Let adjA, A+, AD denote the adjoint matrix, Moore-Penrose inverse and Drazin inverse of complex matrix A. Using singular value decomposition and Jordan decomposition of the matrix and a limit process, it is proved that (adjA)+=adj(A+) and (adjA)D=adj(AD), and showed that A+ and AD are a complex semi-positive subdefinite matrix and A+=AD when A be a complex semi-positive subdefinite matrix.

关 键 词：伴随阵 MOORE-PENROSE逆 DRAZIN逆 复亚半正定阵 

分 类 号：O156.21[理学—数学]