A characterization for the W-weighted Drazin inverse and a Cramer rule for the W-weighted Drazin inverse solution

摘要

We establish characterization for the W-weighted Drazin inverse of an arbitrary rectangular matrix which reduces to the well-known result if the matrix is nonsingular. Also, a Cramer rule for finding the unique W-weighted Drazin inverse solution x∈R[(AW)k1] of special restricted linear equationsWAWx=b,b∈R[(WA)k2]is presented, and reduces to the classical Cramer rule if A is invertible.