Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers

AbstractIn this paper, we investigate the condition number of Drazin inverse and Drazin-inverse solution of singular linear system Ax=b, where A is a n×n rank-deficient matrix and b a real vector of size n, x a real vector. Let α and β be two positive real numbers, when we consider the weighted Frobenius norm ∥[αA,βb]∥P,Q(F) on the data we get the formula of condition number of the Drazin-inverse solution of singular linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, the componentwise perturbation is also investigated