The (anti‐)η$$ \eta $$‐Hermitian solution to a novel system of matrix equations over the split quaternion algebra

Author:

Gao Zi‐Han1,Wang Qing‐Wen12ORCID,Xie Lv‐ming1

Affiliation:

1. Department of Mathematics and Newtouch Center for Mathematics Shanghai University Shanghai People's Republic of China

2. Collaborative Innovation Center for the Marine Artificial Intelligence Shanghai University Shanghai People's Republic of China

Abstract

In comparison to quaternions, split quaternions exhibit a more intricate algebraic structure, characterized by the presence of nontrivial zero factors. Furthermore, in various fields such as geometry and electromagnetism, split quaternions serve as more convenient research tools than quaternions. This paper aims to establish the necessary and sufficient conditions for the existence of (anti‐) ‐Hermitian solutions to a novel system of matrix equations formulated over split quaternions. We also provide the general expression of such solutions when the system is solvable, along with the least squares (anti‐) ‐Hermitian solution in the case of inconsistency. To illustrate the key findings of this paper, numerical examples are presented.

Funder

National Natural Science Foundation of China

Publisher

Wiley

Reference36 articles.

1. On quaternions, or on a new system of imaginaries in algebra;Hamilton W. R.;Lond,1844

2. Removing Gaussian noise for colour images by quaternion representation and optimisation of weights in non‐local means filter

3. SUPG finite element method based on penalty function for lid-driven cavity flow up to $$Re = 27500$$ R e = 27500

4. On systems of algebra involving more than imaginary and on equations of the fifth degree;Cockle J.;Lond,1849

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