可换对合阵组合的可逆性  

On Nonsingularity of Combinations of Three Commuting Involutiory Matrices

作　　者：陈引兰[1] 左可正[1] 谢涛[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：《数学的实践与认识》2014年第17期246-252,共7页Mathematics in Practice and Theory

基　　金：湖北省教育厅重点项目(D20122202);湖北省教育厅青年项目(B20122203)

摘　　要：先讨论两个可换对合阵P,Q线性组合aP+bQ可逆的充分必要条件及可逆时逆矩阵计算公式,再利用矩阵分解,以两种形式讨论两个可换对合阵P,Q组合aI+bP+cQ+dPQ及三个两两可换对合阵P,Q,R组合aI+bP+cQ+dPQ+eR+fPR+gQR+hPQR可逆的充分必要条件及可逆时分别给出逆矩阵计算公式.In this paper, necessary and sufficient conditions for nonsingularity of linear combinations aP ＋ bQof two commuting involutiory matrices P, Qfirtly has been established, then necessary and sufficient conditions for nonsingularity of combinations aI ＋ bP ＋ cQ ＋ dPQof two commuting involutiory matrices P, Qand combinations aI＋bP＋cQ＋dPQ＋eR＋ fPR ＋ gQR ＋ hPQR of three commuting involutiory matrices P, Q, R have been discussed by decomposition of matrices in two kinds of forms, the formulae of the inverse matrices also given respectively.

关 键 词：对合阵 逆矩阵 矩阵分解 矩阵的组合 

分 类 号：O151.21[理学—数学]