幂等矩阵的组合的可逆性

摘要

The paper researches the nonsingularity of combinations aP+bQ-cPQ-dQP- ePQP of two idempotent matrices P and Q(a,b,c,d,e∈(C),a≠0,b≠0). By using the nonsingularity of P-Q and the properties of idempotent matrix, we get some necessary and sufficient conditions of the invertibility of combinations aP+bQ-cPQ-dQP-ePQP of two idempotent matrices P and Q (a,b,c,d,e∈(C),a≠0,b≠0), which generalizes the results of%本文研究了两个幂等矩阵P与Q的组合aP+bQ-cPQ-dQP-ePQP (其中a,b,c,d,e∈(C),a≠0,b≠0)的可逆性. 利用P-Q的可逆性及幂等矩阵的性质,得到了aP+bQ-cPQ-dQP-ePQP可逆的一些充要条件. 推广了J. J.Koliha 和 V.RakoA(c)eviA(c)[1]及Zuo Kezheng[2]的结论.