Minimum Property of Condition Numbers for the Drazin Inverse and Singular Linear Equations


Haifeng Ma




For a singular linear equation Ax = b, x ∈ R(A D), a small perturbation matrix E and a vector δb are given to A and b, respectively. We then have the perturbed singular linear equation (A + E) x = b + δb, x ∈ R[(A + E) D ]. This note is devoted to show the minimum property of the condition numbers on the Drazin inverse A D and the Drazin-inverse solution A D b.