Condition number related with W-weighted Drazin inverse and singular linear systems

In this paper, we introduce a PQ-norm and discuss the condition number of the W-weighted Drazin inverse. We get some results on the condition number with respect to Ad,w and singular linear systems WAWx=b,b∈R((WA)k2), x∈R((AW)k1) which are similar to the regular inverse A−1 and nonsingular linear systems Ax=b.