Abstract:

The matrix represenations of two idempotent operators P and Q under the conditions PQP=0, PQP=P and PQP=PQ are discussed respectively by using the technique of space decompositions of a Hilbert space. The existance and calculation formulas of Drazin inverse of the combinations aP+bQ+cPQ+dQP+eQPQ of the two idempotent operators are obtained.

Key words: idempotent operator; Drazin inverse; combination