@article{Xiao2024, 
author = {Qi Xiao and Jin Zhong},
title = {Characterizations and properties of hyper-dual Moore-Penrose generalized inverse},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {35125-35150},
keywords = {dual matrix, hyper-dual matrix, hyper-dual Moore-Penrose generalized inverse, least-squares property, dual matrix of order n},
url = {https://www.sciopen.com/article/10.3934/math.20241670},
doi = {10.3934/math.20241670},
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.}
}