Тип публикации: статья из журнала
Год издания: 2024
Идентификатор DOI: 10.3934/era.2024083
Аннотация: <jats:p xml:lang="fr"><abstract> 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.
Журнал: Electronic Research Archive
Выпуск журнала: Т. 32, № 3
Номера страниц: 1822-1843
ISSN журнала: 26881594
Издатель: American Mathematical Society