The group inverse of the combinations of two idempotent matrices

摘要

In this article, we discuss the group inverse of aP + bQ + cPQ + dQP + ePQP + fQPQ + gPQPQ of idempotent matrices P and Q, where a, b, c, d, e, f, g ∈ C and a ≠ 0, b ≠ 0, put forward its explicit expressions, and some necessary and sufficient conditions for the existence of the group inverse of aP + bQ + cPQ.