The projection m -weak group inverse
S. B. Malik, D. E. Ferreyra, Fabián Eduardo Levis, Valentina Orquera · Linear and Multilinear Algebra · 2025
This paper introduces the projection m-weak group inverse (or P-m-WG inverse) for square complex matrices as a linear combination of the m-WG inverse A◯wm and its associated projectors A◯wmA and AA◯wm. We establish the uniqueness of the P-m-WG inverse for any matrix with an arbitrary index and provide several characterizations and properties of this generalized inverse. We explore the connections between the P-m-WG inverse of a matrix and it's other known generalized inverses by using the core-EP decomposition of the matrix.