Characterization of the W-weighted Drazin inverse over the quaternion skew field with applications

Abstract

Abstract. A characterization of the W-weighted Drazin inverse as well as some determinantal representations of the W-weighted Drazin inverse over the quaternion skew filed are derived. Moreover, a Cramer's rule for finding the unique solution of a class of restricted quaternion matrix equations is obtained.

Determinantal Representations of the Quaternion Core Inverse and Its Generalizations

“…[17][18][19][20][21][22][23][24][25][26][27][28]) and by other researchers (see, e.g. [40][41][42][43][44]).…”

Cramer’s rules for the system of quaternion matrix equations withη-Hermicity

“…[44][45][46][47][48][49][50][51][52][53][54][55][56][57]) and other researchers (see, e.g. [58][59][60][61]). In particular, determinantal representations of systems like to (1) have been recently explored in [53,55,56,61].…”

Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field

“…are matrices whose columns form bases for N ((WA) k2 ) and N ((AW) k * 1 ), respectively. Recently, within the framework of a theory of the column and row determinants Song [28] has considered the characterization of the W-weighted Drazin inverse over the quaternion skew and presented a Cramer's rule of the restricted matrix equation,…”

“…Cramer's rule for the W-weighted Drazin inverse solutions, in particular, have been derived in [27] for singular linear equations and in [26] for a class of restricted matrix equations. Recently, within the framework of the theory of the column-row determinants Song [28] has first obtained a determinantal representation of the W-weighted Drazin inverse and Cramer's rule of a class of restricted matrix equations over the quaternion algebra. But in obtaining, he has used auxiliary matrices other than that are given.…”