On the general solutions to some systems of quaternion matrix equations

He, Zhuo-Heng; Wang, Meng; Liu, Xin

doi:10.1007/s13398-020-00826-2

Cited by 15 publications

(4 citation statements)

References 36 publications

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“…They presented these findings in terms of the Moore-Penrose inverse of certain given matrices. The resulting equation has wide applications in the linear matrix equations field, see [7,[34][35][36][37][38][39][40]. He and Meng [41] derived the rank equalities solvability conditions for the following quaternion matrix equation with two different restrictions:…”

Section: Introductionmentioning

confidence: 99%

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

Mehany

Wang

2022

Symmetry

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The current study investigates the solvability conditions and the general solution of three symmetrical systems of coupled Sylvester-like quaternion matrix equations. Accordingly, the necessary and sufficient conditions for the consistency of these systems are determined, and the general solutions of the systems are thereby deduced. An algorithm and a numerical example are constructed over the quaternions to validate the results of this paper.

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Section: Introductionmentioning

confidence: 99%

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

Mehany

Wang

2022

Symmetry

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“…Many problems in systems and control theory can be reduced to solving systems of quaternion matrix equations (e.g. [6]- [16], [26]).…”

Section: Introductionmentioning

confidence: 99%

The η-Hermitian solutions to some systems of real quaternion matrix equations

Zhang

2022

Filomat

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Let Hmxn be the set of all m x n matrices over the real quaternion algebra. We call that A ? Hnxn is ?-Hermitian if A = A?* where A?* = -?A*?,? ? {i,j,k},i,j,k are the quaternion units. In this paper, we derive some solvability conditions and the general solution to a system of real quaternion matrix equations. As an application, we present some necessary and sufficient conditions for the existence of an ?-Hermitian solution to some systems of real quaternion matrix equations. We also give the expressions of the general ?-Hermitian solutions to these systems when they are solvable. Some numerical examples are given to illustrate the results of this paper.

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“…Among concerns with a quaternion matrix equation are solvability conditions, general solutions, minimum norm least squares solutions, various symmetric solutions, the maximal and minimal ranks of solutions, etc. (e.g., 4–32 ).…”

Section: Introductionmentioning

confidence: 99%

Solvability conditions and general solutions to some quaternion matrix equations

Wang

2021

Math Methods in App Sciences

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Since quaternion and quaternion matrices have applications in color image processing, 1 quantum mechanics, 2 signal processing, 3 etc., research on quaternion matrix equations has been actively ongoing for more recent years. Among concerns with a quaternion matrix equation are solvability conditions, general solutions, minimum norm least squares solutions, various symmetric solutions, the maximal and minimal ranks of solutions, etc. (e.g., ).Rodman gave a necessary and sufficient conditions for the existence of a unique solution to the quaternion matrix equation AX + XB = C. 5, page 117 Wang 6 presented bisymmetric and centrosymmetric solutions to some systems of quaternion matrix equations. Kyrchei 7 provided the minimum norm least squares solutions of some quaternion matrix Abbreviations: ANA, anti-nuclear antibodies; APC, antigen-presenting cells; IRF, interferon regulatory factor.

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On the general solutions to some systems of quaternion matrix equations

Cited by 15 publications

References 36 publications

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

The η-Hermitian solutions to some systems of real quaternion matrix equations

Solvability conditions and general solutions to some quaternion matrix equations

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