The generalized inverse of the quaternion tensor via the M-product

Authors

  • Hongwei Jin School of Mathematical Sciences; Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, PR China
  • Yuzhen Wang School of Mathematical Sciences, Guangxi Minzu University, Nanning, PR China
  • Shaowu Huang School of Mathematics and Finance, Putian University, Putian, PR China
  • Vasilios N. Katsikis Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

DOI:

https://doi.org/10.3842/umzh.v78i9-10.9032

Keywords:

M-Product, Tensors, Moore-Penrose inverse, Tensor equations, Reverse order law

Abstract

UDC 512.64

We study the expressions for the Moore–Penrose inverse of the quaternion tensor under the M-product. Some equivalent characterizations of the Moore–Penrose inverse are given. Moreover, we prove that the Moore–Penrose inverse is a unique solution to some  equations. In addition, we not only define the range and null space of the quaternion tensor but  also characterize the Drazin inverse of the quaternion tensor. Furthermore, some equivalent expressions of the left and right inverses along the quaternion tensor are given. Finally, the applications to  multilinear systems are presented.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 9-10, 2026.

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Published

19.09.2026

Issue

Vol. 78 No. 9-10 (2026)

Section

Research articles