矩阵的两个幂等矩阵组合的可逆性

摘要

利用幂等矩阵的性质及两个幂等矩阵的和与差的可逆性,研究了两个幂等矩阵P,Q在条件(PQ)2=PQ下,它们的组合T=aP +bQ+cPQ+ dQP+ ePQP+ fQPQ+ g(QP)2,(a,b,c,d,e,f,g∈C,ab≠0)的可逆性,并给出它的求逆公式.%By using the nonsingularity of difference and sum of two idempotent matricesP、Q,we study the invertibility of the combination T =aP + bQ +cPQ +dQP +ePQP+fQPQ+g(PQ)2,(a,b,c,d,e,f,g ∈ C,ab≠0) under the condition of(PQ)2 =PQ.Furthermore,the expression of its inverse is provided in this paper.