Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field

Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field

By using determinantal representations of the W-weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the W-weighted Drazin inverse solutions (analogs of Cramer’s rule...

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Main Author: Ivan I. Kyrchei
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2016/8673809
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spelling doaj-e435342d3116490fa492efdf61b782cd2020-11-24T23:07:08ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472016-01-01201610.1155/2016/86738098673809Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew FieldIvan I. Kyrchei0Pidstrygach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Lviv 79060, UkraineBy using determinantal representations of the W-weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the W-weighted Drazin inverse solutions (analogs of Cramer’s rule) of the quaternion matrix equations WAWX=D, XWBW=D, and W1AW1XW2BW2=D.http://dx.doi.org/10.1155/2016/8673809
collection DOAJ
language English
format Article
sources DOAJ
author Ivan I. Kyrchei
spellingShingle Ivan I. Kyrchei
Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field
Mathematical Problems in Engineering
author_facet Ivan I. Kyrchei
author_sort Ivan I. Kyrchei
title Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field
title_short Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field
title_full Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field
title_fullStr Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field
title_full_unstemmed Explicit Determinantal Representation Formulas of W-Weighted Drazin Inverse Solutions of Some Matrix Equations over the Quaternion Skew Field
title_sort explicit determinantal representation formulas of w-weighted drazin inverse solutions of some matrix equations over the quaternion skew field
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2016-01-01
description By using determinantal representations of the W-weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the W-weighted Drazin inverse solutions (analogs of Cramer’s rule) of the quaternion matrix equations WAWX=D, XWBW=D, and W1AW1XW2BW2=D.
url http://dx.doi.org/10.1155/2016/8673809
work_keys_str_mv AT ivanikyrchei explicitdeterminantalrepresentationformulasofwweighteddrazininversesolutionsofsomematrixequationsoverthequaternionskewfield
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