两个幂等算子线性组合的Drazin逆

Drazin Inverse of Linear Combinations Associated with Two Idempotent Operators

主要讨论两个幂等算子P和Q的线性组合aP+bQ+cPQ+dQP在条件PQP=QP下Drazin逆的存在性,并分别在θ=a+b+c+d=0和θ=a+b+c+d≠0的情况下将其Drazin逆用P,Q,PQ,QP,QPQ的线性组合表示出来.最后,给出相应的例子验证结论的合理性.

The existence for the Drazin inverse of a linear combination aP＋bQ＋cPQ＋dQP associated two idempotent P and Q is discussed under the condition PQP,In the case of θ=a＋b＋c＋d=0 or θ=a＋b＋c＋d≠0,its Drazin inverses are represented in terms of a linear combination of P,Q,PQ,QP,PQP respectively. Furthermore, an example is given to illustrate the main results.