Moore-Penrose inverses for matrices over some Noetherian rings
type: Item
instance of: scholarly article
title: Moore-Penrose inverses for matrices over some Noetherian rings
zbMATH Open document ID: 0536.15004
DOI: 10.1016/0022-4049(84)90085-9
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 3851285
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: Noetherian generalizations
zbMATH Keywords: Penrose equations
zbMATH Keywords: Noetherian rings
zbMATH Keywords: principal ideal domain
author: R. Puystjens
reviewed by: Joseph A. Ball
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90085-9
OpenAlex ID: W2017806315
cites work: Integral generalized inverses of integral matrices
cites work: Q5834678
cites work: Q5540535
cites work: Q3897153
cites work: The Moore-Penrose inverse of a morphism with factorization
cites work: The Moore-Penrose inverse of a morphism in an additive category
description: scientific article; zbMATH DE number 3851285