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

We establish characterization for the W-weighted Drazin inverse of an arbit rary rectangular matrix which reduces to the well-known result if the matri x is nonsingular. Also, a Cramer rule for finding the unique W-weighted Dra zin inverse solution x is an element of R[(AW)(k1)] of special restricted l inear equations WAWx = b, b is an element of R[(WA)(k2)] is presented, and reduces to the classical Cramer rule if A is invertible. (C) 2002 Elsevier Science Inc. All rights reserved.