Condition number related with generalized inverse AT,S(2) and constrained linear systems

In this paper, we introduce a PQ-norm and discuss the condition number of the generalized inverse AT,S(2). We get some results on the condition numbers with respect to AT,S(2) and constrained linear systems Ax=b,x∈T which are similar to the regular inverse A−1 and nonsingular linear systems Ax=b. Finally, we investigate the structured perturbation of the generalized inverse AT,S(2).