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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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/6294672 |
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| _version_ | 1849406277997821952 |
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| author | Ivan I. Kyrchei |
| author_facet | Ivan I. Kyrchei |
| author_sort | Ivan I. Kyrchei |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-4b657b61493f4cc8a9181582a921b1f5 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4b657b61493f4cc8a9181582a921b1f52025-08-20T03:36:26ZengWileyJournal 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 |
| spellingShingle | Ivan I. Kyrchei Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations Journal of Mathematics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2018/6294672 |
| work_keys_str_mv | AT ivanikyrchei determinantalrepresentationsofsolutionsandhermitiansolutionstosomesystemoftwosidedquaternionmatrixequations |