On generalized inverses of \(m \times n\) matrices over a pseudoring
The authors give a characterization of matrices having generalized inverses. More specifically, they introduce and study a space decomposition method, and prove that a matrix is decomposable if and only if it has a generalized inverse. Finally, they establish necessary and sufficient conditions for a matrix to possess various types of \(g\)-inverses, including the Moore-Penrose inverse.
scientific article; zbMATH DE number 7438396