Minimum property of condition numbers for the Drazin inverse and singular linear equations

Abstract

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