两个幂等矩阵组合的Drazin逆

The Drazin Inverse of Combinations of Two Idempotent Matrices

证明了两个不同的非零幂等矩阵P，Q的组合A=aP＋bQ＋cPQ＋dQP＋ePQP＋fQPQ＋g（PQ）2＋h（Qp）2＋i（QP）2Q，（其中a，b，c，d，e，f，g，h，i∈ C,a,b≠0）在条件（PQ）^2P=（pQ）^2下存在Drazin逆，并且给出其Drazin逆计算公式．

The Drazin inverse of combinations A=aP＋bQ＋cPQ＋dQP＋ePQP＋fQPQ＋g（PQ）2＋h（Qp）2＋i（QP）2Q,of two nonzero different idempotent matrices P and Q under the condition （PQ）^2P=（pQ）^2is proved, where a, b, c, d, e, f, g, h, i∈C,a,b≠0.The formulae of its Drazin inverse is also presented.