Explicit determinantal representation formulas of \(W\)-weighted Drazin inverse solutions of some matrix equations over the quaternion skew field (Q1793702)

Summary: By using determinantal representations of the \(W\)-weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the \(W\)-weighted Drazin inverse solutions (analogs of Cramer's rule) of the quaternion matrix equations \(\mathbf{W} \mathbf{A} \mathbf{W} \mathbf{X} = \mathbf{D}\), \(\mathbf{X} \mathbf{W} \mathbf{B} \mathbf{W} = \mathbf{D}\), and \(\mathbf{W}_1 \mathbf{A} \mathbf{W}_1 \mathbf{X} \mathbf{W}_2 \mathbf{B} \mathbf{W}_2 = \mathbf{D}\).