Generalized inverses
type: Item
instance of: scholarly article
title: Generalized inverses
author: Dragan S. Djordjević
publication date: 2021-09-03T00:00:00Z
review text: This is a brief survey on generalized inverses of operators. The notions of inner and outer generalized inverses of bounded linear operators on Banach spaces, as well as the Moore-Penrose inverse of closed range bounded linear operators on Hilbert spaces, are presented using \(2 \times 2\) operator matrices. As an application, results on the reverse order law are proved. The existence of least squares solutions of linear equations is presented, as another application. The notion of Drazin inverse is posed in the setting of a complex unital Banach algebra, and by using properties of the spectrum and vector valued analytic functions, wherein operator matrices are replaced by the spectral idempotent. For the entire collection see [Zbl 1468.53002].
reviewed by: K. C. Sivakumar
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 47-02
zbMATH DE Number: 7391048
zbMATH Keywords: Drazin inverse
zbMATH Keywords: generalized inverses
zbMATH Keywords: inner and outer inverse
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: reverse order law
MaRDI profile type: Publication
full work available at URL: giq-22-2021-13-32
OpenAlex ID: W4205319120
cites work: Generalized inverses. Theory and applications.
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cites work: Q3873026
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cites work: Q5849795
cites work: Q3231532
cites work: Generalized inverses: theory and computations
DOI: 10.7546/GIQ-22-2021-13-32
description: scientific article; zbMATH DE number 7391048