Determinantal Representations of the Core Inverse and Its Generalizations with Applications
In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derive...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/1631979 |
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| author | Ivan I. Kyrchei |
| author_facet | Ivan I. Kyrchei |
| author_sort | Ivan I. Kyrchei |
| collection | DOAJ |
| description | In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given. |
| format | Article |
| id | doaj-art-8c7f8652690d4595929029b6ac85d155 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8c7f8652690d4595929029b6ac85d1552025-02-03T07:24:39ZengWileyJournal of Mathematics2314-46292314-47852019-01-01201910.1155/2019/16319791631979Determinantal Representations of the Core Inverse and Its Generalizations with ApplicationsIvan I. Kyrchei0Pidstrygach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Lviv, UkraineIn this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given.http://dx.doi.org/10.1155/2019/1631979 |
| spellingShingle | Ivan I. Kyrchei Determinantal Representations of the Core Inverse and Its Generalizations with Applications Journal of Mathematics |
| title | Determinantal Representations of the Core Inverse and Its Generalizations with Applications |
| title_full | Determinantal Representations of the Core Inverse and Its Generalizations with Applications |
| title_fullStr | Determinantal Representations of the Core Inverse and Its Generalizations with Applications |
| title_full_unstemmed | Determinantal Representations of the Core Inverse and Its Generalizations with Applications |
| title_short | Determinantal Representations of the Core Inverse and Its Generalizations with Applications |
| title_sort | determinantal representations of the core inverse and its generalizations with applications |
| url | http://dx.doi.org/10.1155/2019/1631979 |
| work_keys_str_mv | AT ivanikyrchei determinantalrepresentationsofthecoreinverseanditsgeneralizationswithapplications |