【摘要】 运用幂等矩阵核空间的性质证明复数域上两个非零幂等矩阵P,Q的组合a₁P+b₁Q+a₂PQ+b₂QP+a₃PQP+b₃QPQ+a₄PQPQ+b₄QPQP+a₅PQPQP+b₅QPQPQ+a₆PQPQPQ（其中a_i,b_j∈C（1≤i≤6,1≤j≤5）且a₁b₁≠0）在条件（PQ）³=（QP）³下的秩与系数的选取无关,进而证明其群逆的存在性,并得到了组合aP+bQ+cPQ+dQP的群逆计算公式.更多还原

【Abstract】 With the aid of the properties of the null space of idempotent matrices,the rank of the combination a₁P +b₁Q +a₂PQ +b₂QP +a₃PQP +b₃QPQ +a₄PQPQ +b₄QPQP +a₅PQPQP +b₅QPQPQ +a₆PQPQPQ of two nonzero idempotent matrices P and Q over the complex field C,where a_i,b_j∈ C（1≤i≤6,1≤j≤5）and a₁b₁≠0,was proved to be independent with the choice of its coefficients and the group inverse of the combination was furtherly verified to exist under the condition（PQ）³=（QP）³.Moreover,the formula for the group inverse of the combination aP+bQ+cPQ+dQP was also obtained.更多还原