A generalization of the MP-m-WGI (Q6622114)

To solve a system of matrix equations, the author uses a combination of an inner inverse and an \(m\)-WGI (weak group inverse). She also introduces a new type of generalized inverse, called inner-\(m\)-WGI. She demonstrates that inner-CEP and inner-GGI are two specific types of inner-\(m\)-WGI. Various characterizations and representations of the inner-\(m\)-WGI are provided, including the canonical matrix form. Furthermore, she investigates the \(m\)-WG-inner inverse as a dual inner-\(m\)-WGI. By using these results, she is able to prove the solvability of certain systems of equations.