Comment On "Condition Number Of Drazin Inverse And Their Condition Numbers Of Singular Linear Systems"

In this paper,we establish the condition number of Drazin inverse of a singular matrix A,where R(A^k) = R(A^k*) and k = index(A),by the Schur decomposition. Based on this form,the spectral norm and Frobenius norm of relative condition number for the Drazin inverse and level-2 condition number of the Drazin inverse are char-acterized.The sensitivity for the Drazin-inverse solution of singular systems is also presented.We obtain several formulas for the condition number of the Drazin inverse by spectral norm instead of the P-norm,where P is a transformation matrix of the Jordan canonical form of A,thereby improving the earlier work(Wei et al in Applied Mathematics and Computation,vol.146(2003) pp.455-467).