The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra

Si, Kai-Wen; Wang, Qing-Wen

doi:10.3390/sym16040491

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2024

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Cited by 7 publications

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“…To solve our problems in a unified way, we introduce two new real representations of the split quaternion matrices, which are more convenient in solving the eight cases concurrently (see [18]).…”

Section: Real Representationsmentioning

confidence: 99%

Solution to Several Split Quaternion Matrix Equations

Liu,

Shi,

Zhang

2024

Mathematics

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Split quaternions have various applications in mathematics, computer graphics, robotics, physics, and so on. In this paper, two useful, real representations of a split quaternion matrix are proposed. Based on this, we derive their fundamental properties. Then, via the real representation method, we obtain the necessary and sufficient conditions for the existence of solutions to two split quaternion matrix equations. In addition, two experimental examples are provided to show their feasibility.

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Section: Real Representationsmentioning

confidence: 99%

Solution to Several Split Quaternion Matrix Equations

Liu,

Shi,

Zhang

2024

Mathematics

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

Gao,

Wang,

Xie

2024

Math Methods in App Sciences

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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.

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