Determinantal representations of the quaternion core inverse and its generalizations
type: Item
instance of: scholarly article
title: Determinantal representations of the quaternion core inverse and its generalizations
zbMATH Open document ID: 1436.15004
author: Ivan I. Kyrchei
published in: Advances in Applied Clifford Algebras
publication date: 2019-11-27T00:00:00Z
review text: The core inverse was introduced in [\textit{O. M. Baksalary} and \textit{G. Trenkler}, Linear Multilinear Algebra 58, No. 5--6, 681--697 (2010; Zbl 1202.15009)]. In this paper, the author investigates the notions of core inverse, core-EP inverse, DMP inverse, and CMP inverse over the quaternion skew-field. Indeed, he studies a direct method to compute their determinantal representations by using column and row noncommutative determinants previously introduced by the author in [Appl. Math. Comput. 219, No. 14, 7632--7644 (2013; Zbl 1291.15040)]. As a special case, the author provides determinantal representations for complex matrices as well. Some useful examples to illustrate the main results are given.
reviewed by: Kamran Sharifi
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 7137699
zbMATH Keywords: core inverse
zbMATH Keywords: core-EP inverse
zbMATH Keywords: generalized inverse
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: Drazin inverse
zbMATH Keywords: quaternion matrix
zbMATH Keywords: noncommutative determinant
MaRDI profile type: Publication
full work available at URL: s00006-019-1024-6
OpenAlex ID: W2982075377
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Wikidata QID: Q126975872
DOI: 10.1007/S00006-019-1024-6
description: scientific article; zbMATH DE number 7137699