A Cramer rule for solution of the general restricted matrix equation

摘要

A Cramer rule for finding the unique W-weighted Drazin inverse solution of a class of restricted matrix equationsWAWXWBW=D,R(X)⊂R[(AW)k1],N(X)⊃N[(WB)k̃2]is presented, and the results in [Linear Algebra Appl. 116 (1989) 27, Appl. Math. Comput. 125 (2002) 303] can be deduced from this paper. Where A∈Cm×n, W∈Cn×m, Ind(AW)=k1, B∈Cp×q, W∈Cq×p, Ind(WB)=k̃2, and D∈Cn×p.