A Quaternion Matrix Equation with Two Different Restrictions

He, Zhuo-Heng; Wang, Meng

doi:10.1007/s00006-021-01122-x

Cited by 12 publications

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References 47 publications

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“…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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“…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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Decomposition for a Quaternion Tensor Triplet with Applications

Navasca

Wang

2022

Adv. Appl. Clifford Algebras

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A Quaternion Matrix Equation with Two Different Restrictions

Cited by 12 publications

References 47 publications

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

Solvability conditions and general solutions to some quaternion matrix equations

Decomposition for a Quaternion Tensor Triplet with Applications

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