Characterizations and properties of hyper-dual Moore-Penrose generalized inverse
In this paper, the definition of the hyper-dual Moore-Penrose generalized inverse of a hyper-dual matrix is introduced. Characterizations for the existence of the hyper-dual Moore-Penrose generalized inverse are given, and a formula for the hyper-dual Moore-Penrose generalized inverse is presented w...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241670 |
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| author | Qi Xiao Jin Zhong |
| author_facet | Qi Xiao Jin Zhong |
| author_sort | Qi Xiao |
| collection | DOAJ |
| description | In this paper, the definition of the hyper-dual Moore-Penrose generalized inverse of a hyper-dual matrix is introduced. Characterizations for the existence of the hyper-dual Moore-Penrose generalized inverse are given, and a formula for the hyper-dual Moore-Penrose generalized inverse is presented whenever it exists. Least-squares properties of the hyper-dual Moore-Penrose generalized inverse are discussed by introducing a total order of hyper-dual numbers. We also introduce the definition of a dual matrix of order $ n $. A necessary and sufficient condition for the existence of the Moore-Penrose generalized inverse of a dual matrix of order $ n $ is given. |
| format | Article |
| id | doaj-art-1c15aae5e3f949a28e28145ebcd18c3c |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-1c15aae5e3f949a28e28145ebcd18c3c2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912351253515010.3934/math.20241670Characterizations and properties of hyper-dual Moore-Penrose generalized inverseQi Xiao0Jin Zhong1Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, ChinaFaculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, ChinaIn this paper, the definition of the hyper-dual Moore-Penrose generalized inverse of a hyper-dual matrix is introduced. Characterizations for the existence of the hyper-dual Moore-Penrose generalized inverse are given, and a formula for the hyper-dual Moore-Penrose generalized inverse is presented whenever it exists. Least-squares properties of the hyper-dual Moore-Penrose generalized inverse are discussed by introducing a total order of hyper-dual numbers. We also introduce the definition of a dual matrix of order $ n $. A necessary and sufficient condition for the existence of the Moore-Penrose generalized inverse of a dual matrix of order $ n $ is given.https://www.aimspress.com/article/doi/10.3934/math.20241670dual matrixhyper-dual matrixhyper-dual moore-penrose generalized inverseleast-squares propertydual matrix of order $ n $ |
| spellingShingle | Qi Xiao Jin Zhong Characterizations and properties of hyper-dual Moore-Penrose generalized inverse AIMS Mathematics dual matrix hyper-dual matrix hyper-dual moore-penrose generalized inverse least-squares property dual matrix of order $ n $ |
| title | Characterizations and properties of hyper-dual Moore-Penrose generalized inverse |
| title_full | Characterizations and properties of hyper-dual Moore-Penrose generalized inverse |
| title_fullStr | Characterizations and properties of hyper-dual Moore-Penrose generalized inverse |
| title_full_unstemmed | Characterizations and properties of hyper-dual Moore-Penrose generalized inverse |
| title_short | Characterizations and properties of hyper-dual Moore-Penrose generalized inverse |
| title_sort | characterizations and properties of hyper dual moore penrose generalized inverse |
| topic | dual matrix hyper-dual matrix hyper-dual moore-penrose generalized inverse least-squares property dual matrix of order $ n $ |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241670 |
| work_keys_str_mv | AT qixiao characterizationsandpropertiesofhyperdualmoorepenrosegeneralizedinverse AT jinzhong characterizationsandpropertiesofhyperdualmoorepenrosegeneralizedinverse |