Condition numbers for the outer inverse and constrained singular linear system

In this paper, we investigate the condition number of the outer inverse AT,S(2) and outer inverse AT,S(2) solution of constrained linear system Ax = b, x ∈ T, where A is a real m × n matrix, b and x are real vectors, T is a subspace. Let α and β   be two positive real numbers, when we consider the weighted Frobenius norm ∥[αA,βb]∥QP(F) on the data we get the formula of condition number for the outer inverse AT,S(2) solution of constrained linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, and the componentwise perturbation is also investigated.