Condensed Cramer rule for solving restricted matrix equations (Q864772)

A Cramer rule for solving restricted matrix equations of the kind \(WAWX\widetilde{W} B\widetilde{W}=D\), \(R(X)\subset R[(AW)^{k_1}]\), \(N(X)\supset N[(\tilde{W}B)^{k_2}]\) was presented by \textit{G. Wang} and \textit{J. Sun} [Appl. Math. Comput. 154, 415--422 (2004; Zbl 1055.15024)]. The present paper contains a more condensed Cramer rule for the solutions of such equations. The results of the following two papers are special cases of the ones of the present paper: \textit{G. Wang} and \textit{Z. L. Xu} [Appl. Math. Comput. 162, 329--338 (2005; Zbl 1062.15008)] and \textit{Chao Gu}, \textit{G. R. Wang} and \textit{Z. L. Xu} [Appl. Math. Comput. 176, 237--244 (2006; Zbl 1092.65024)].