2024
DOI: 10.3390/sym16030361
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The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations

Yue Zhang,
Qing-Wen Wang,
Lv-Ming Xie

Abstract: This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples.

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Cited by 10 publications
(4 citation statements)
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“…indicating that (X 00 σ i ,X 01 σ i ) is a pair of solutions to the system (23). From (7) of proposition 1, we can easily get that (U n (X i 00…”
Section: Corollary 1 Letmentioning
confidence: 97%
See 1 more Smart Citation
“…indicating that (X 00 σ i ,X 01 σ i ) is a pair of solutions to the system (23). From (7) of proposition 1, we can easily get that (U n (X i 00…”
Section: Corollary 1 Letmentioning
confidence: 97%
“…) are also pairs of symmetric solutions to the system (23). Then, so is (Y 0 , Y 1 ), where By direct computation, we have…”
Section: Corollary 1 Letmentioning
confidence: 99%
“…On the other hand, very recently, Chen, Wang, and Xie (2024) [25] presented the solvability and the expression of general solutions to the classical matrix equation AXB = C regarding dual quaternions. In a parallel development, Zhang, Wang, and Xie (2024) [26] investigated the Hermitian solution of a system of matrix equations over commutative quaternions, which consists of AXB = C, one generalized Sylvester equation DXE + FYG + HZ + W I = J, and some additional equations of the forms KX = L and XM = N. It is well-known that the matrix equation AXB = C plays a crucial role in image processing. These may also provide an opportunity for further research on image processing based on generalized quaternions.…”
Section: Conclusion and Prospectsmentioning
confidence: 99%
“…It is well established that linear matrix equations have been a focal point in matrix theory and its applications. Numerous researchers have devoted attention to studying the solutions of matrix equations [22][23][24][25][26]. The matrix equation…”
Section: Introductionmentioning
confidence: 99%