Explicit Determinantal Representation Formulas of W -Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field

Abstract

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 W A W X = D, X W B W = D, and W 1 A W 1 X W 2 B W 2 = D.