Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations

Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations

Within the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer’s rule) of solutions and Hermitian solutions to the system of two-sided quaternion matrix equations A1XA1⁎=C1 and A2XA2⁎=C2. Since...

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Main Author: Ivan I. Kyrchei
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2018/6294672
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spelling doaj-4b657b61493f4cc8a9181582a921b1f52020-11-25T00:45:16ZengHindawi LimitedJournal of Mathematics2314-46292314-47852018-01-01201810.1155/2018/62946726294672Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix EquationsIvan I. Kyrchei0Pidstrygach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Lviv, UkraineWithin the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer’s rule) of solutions and Hermitian solutions to the system of two-sided quaternion matrix equations A1XA1⁎=C1 and A2XA2⁎=C2. Since the Moore-Penrose inverse is a necessary tool to solve matrix equations, we use determinantal representations of the Moore-Penrose inverse previously obtained by the theory of row-column determinants.http://dx.doi.org/10.1155/2018/6294672
collection DOAJ
language English
format Article
sources DOAJ
author Ivan I. Kyrchei
spellingShingle Ivan I. Kyrchei
Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations
Journal of Mathematics
author_facet Ivan I. Kyrchei
author_sort Ivan I. Kyrchei
title Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations
title_short Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations
title_full Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations
title_fullStr Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations
title_full_unstemmed Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations
title_sort determinantal representations of solutions and hermitian solutions to some system of two-sided quaternion matrix equations
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2018-01-01
description Within the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer’s rule) of solutions and Hermitian solutions to the system of two-sided quaternion matrix equations A1XA1⁎=C1 and A2XA2⁎=C2. Since the Moore-Penrose inverse is a necessary tool to solve matrix equations, we use determinantal representations of the Moore-Penrose inverse previously obtained by the theory of row-column determinants.
url http://dx.doi.org/10.1155/2018/6294672
work_keys_str_mv AT ivanikyrchei determinantalrepresentationsofsolutionsandhermitiansolutionstosomesystemoftwosidedquaternionmatrixequations
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