Abstract
The notion of the generalized core-EP (g-core-EP) inverse is defined as a generalization of well-known core-EP inverse to rectangular matrices. The extension is defined using the outer inverse and the Moore-Penrose inverse. Various basic properties, representations and characterizations of the g-core-EP inverse are investigated. The *g-core-EP inverse is introduced and investigated as the dual of g-core-EP inverse. Several integral and limit representations of the g-core-EP and *g-core-EP inverses are considered. Also, applications of the g-core-EP and *g-core-EP inverses in solving some restricted systems of linear equations are considered.
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