Reducible solution to a quaternion tensor equation

doi:10.1007/s11464-020-0865-6

Front. Math. China

2020, Vol. 15

Issue (5) : 1047-1070 https://doi.org/10.1007/s11464-020-0865-6

RESEARCH ARTICLE

Reducible solution to a quaternion tensor equation

Mengyan XIE, Qing-Wen WANG(

)

Department of Mathematics, Shanghai University, Shanghai 200444, China

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Abstract

We establish necessary and sufficient conditions for the existence of the reducible solution to the quaternion tensor equation $A * N ⁢ X * N ⁢ B = C$ via Einstein product using Moore-Penrose inverse, and present an expression of the reducible solution to the equation when it is solvable. Moreover, to have a general solution, we give the solvability conditions for the quaternion tensor equation $A 1 * N ⁢ X 1 * M ⁢ B 1 + A 1 * N ⁢ X 2 * M ⁢ B 2 + A 2 * N ⁢ X 3 * M ⁢ B 2 = C$ , which plays a key role in investigating the reducible solution to $A * N ⁢ X * N ⁢ B = C$ . The expression of such a solution is also presented when the consistency conditions are met. In addition, we show a numerical example to illustrate this result.

Keywords Quaternion tensor quaternion tensor equation Einstein product Moore-Penrose inverse general solution reducible solution

Corresponding Author(s): Qing-Wen WANG

Issue Date: 19 November 2020

Cite this article:

Mengyan XIE,Qing-Wen WANG. Reducible solution to a quaternion tensor equation[J]. Front. Math. China, 2020, 15(5): 1047-1070.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0865-6
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I5/1047

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