Moore-Penrose inverses for matrices over some Noetherian rings
The Moore-Penrose inverse of an \(m\times n\) matrix (over the complex numbers \({\mathbb{C}})\) A can be introduced as the unique solution X of the equations \(AX=P\) and \(XA=Q\), where P is the orthogonal projection onto Im A and Q is the orthogonal projection onto Im X. In the present paper various Noetherian generalizations to the Moore-Penrose inverse are considered; that is, Penrose equations are considered for matrices over some more general Noetherian rings with involution. The most general criterion for existence of a Moore-Penrose inverse is set down from a categorical point of view; this calls for the given morphism to have a certain factored form. This is then applied to the case of matrices over a principal ideal domain.
scientific article; zbMATH DE number 3851285