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The η-Anti-Hermitian Solution to a System of Constrained Matrix Equations over the Generalized Segre Quaternion Algebra

Bai-Ying Ren, Qing‐Wen Wang, Xueying Chen

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Abstract

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the η-anti-Hermitian solution to a system of constrained matrix equations over the generalized Segre quaternion algebra. We also obtain the expression of the general η-anti-Hermitian solution to the system when it is solvable. Finally, we provide a numerical example to verify the main results of this paper.

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What this paper is about

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the η-anti-Hermitian solution to a system of constrained matrix equations over the generalized Segre quaternion algebra. We also obtain the expression of the general η-anti-Hermitian solution to the system when it is solvable. Finally, we provide a numerical example to verify the main results of this paper.

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Available abstract

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the η-anti-Hermitian solution to a system of constrained matrix equations over the generalized Segre quaternion algebra. We also obtain the expression of the general η-anti-Hermitian solution to the system when it is solvable. Finally, we provide a numerical example to verify the main results of this paper.

Key concepts: Quaternion, Hermitian matrix, Quaternion algebra, Algebra over a field, Mathematics, Matrix (chemical analysis), Matrix algebra, Pure mathematics

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