Characterizations and properties of hyper-dual Moore-Penrose generalized inverse

Qi Xiao; Jin Zhong; Qi Xiao; Jin Zhong

doi:10.3934/math.20241670

AIMS Mathematics

2024, Volume 9, Issue 12: 35125-35150. doi: 10.3934/math.20241670

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Research article

Characterizations and properties of hyper-dual Moore-Penrose generalized inverse

Qi Xiao ,
Jin Zhong ^,

Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Received: 10 October 2024 Revised: 30 November 2024 Accepted: 09 December 2024 Published: 16 December 2024
MSC : 15A09, 15A24, 15B33

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.
- dual matrix,
- hyper-dual matrix,
- hyper-dual Moore-Penrose generalized inverse,
- least-squares property,
- dual matrix of order $ n $
Citation: Qi Xiao, Jin Zhong. Characterizations and properties of hyper-dual Moore-Penrose generalized inverse[J]. AIMS Mathematics, 2024, 9(12): 35125-35150. doi: 10.3934/math.20241670

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Abstract

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.

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