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

Authors:
Yimin Wei
Affiliations:
Department of Mathematics and Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, People's Republic of China
Venue:
Applied Mathematics and Computation
Year:
2002

Citing 7
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Abstract

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 equations WAWx = b, b ∈ R[(WA)k2] is presented, and reduces to the classical Cramer rule if A is invertible.