Determinantal Representations of the Solutions to Systems of Generalized Sylvester Equations

Liu, Xin; Song, Guang-Jing; Zhang, Yang

doi:10.1007/s00006-019-1038-0

Cited by 8 publications

(6 citation statements)

References 37 publications

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“…Similarly, we can show that (39) to (41) are equivalent to (18) to (20), respectively. Now, we turn to prove that (42) is equivalent to (19). It follows from the Lemma 1 and elementary transformations that…”

Section: It Follows From Lemma 1 and Elementary Transformations Thatmentioning

confidence: 94%

“…Wang [16] investigated (3) over an arbitrary regular ring with an identity element. Due to the wide applications of quaternions, the investigations on Sylvester-type matrix equations have been extended to H in the last decade (see, e.g., [17][18][19][20][21][22][23][24]). They are applied for signal processing, color-image processing, and maximal invariant semidefinite or neutral subspaces, etc.…”

Section: Introductionmentioning

confidence: 99%

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A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application

2022

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Section: It Follows From Lemma 1 and Elementary Transformations Thatmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application

2022

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“…Up to this point, matrix equations have witnessed a large number of papers proposing various methods for solving some matrix equations (see, e.g., [5][6][7][8][9][10]). The classical matrix equation…”

Section: Introductionmentioning

confidence: 99%

Dual Quaternion Matrix Equation AXB = C with Applications

Chen,

Wang,

Xie

2024

Symmetry

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Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C regarding the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

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“…Meanwhile, Liu et al [31] derive the determinantal representations of the general solution to (6). The solvability conditions and the general solution formulas for the matrix equations:…”

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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Determinantal Representations of the Solutions to Systems of Generalized Sylvester Equations

Cited by 8 publications

References 37 publications

A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application

A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application

Dual Quaternion Matrix Equation AXB = C with Applications

Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations

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