The m-weak group inverse for rectangular matrices

An extension of the m -weak group inverse (or m-WGI) on the set of rectangular matrices is provided to solve some systems of matrix equations. The extension is termed as the W -weighted m-WGI (or W-m-WGI). The W-m-WGI presents a new, wider class of generalized inverses which involves some already defined generalized inverses, such as the m-WGI, W -weighted weak group, and W -weighted Drazin inverse. Basic properties and diverse characterizations are proved for W-m-WGI. Several expressions for computing W-m-WGI are proposed in terms of known generalized inverses and projectors, as well as its limit and integral representations. The W-m-WGI class is utilized to solve some linear matrix equations and express their general solutions. Some new properties of the weighted generalized group inverse and recognized properties of the W -weighted Drazin inverse are obtained as corollaries. Numerical and symbolic test examples are presented to verify the obtained results.