A constrained system of matrix equations

Xu, Yangfan; Wang, Qingwen; Liu, Long-Sheng; Mehany, Mahmoud Saad

doi:10.1007/s40314-022-01873-8

Cited by 16 publications

(6 citation statements)

References 26 publications

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“…Nowadays, quaternion tensors are often used to solve problems in quantum mechanics, control theory, linear modeling, etc. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

2022

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In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system A1*NX1=C1,A1*NX2+A2*NX3=C2,E1*NX1*MF1+E1*NX2*MF2+E2*NX3*MF2=D by using the Moore–Penrose inverses of block tensors. As an application, we discuss the quaternion tensor system A*NX=C,E*NX*MF=D for minimum-norm least squares reducible solutions. To illustrate the results, we present an algorithm and a numerical example.

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Section: Introductionmentioning

confidence: 99%

The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

2022

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“…This is based on the various uses of quaternions, rank characterizations of some matrix expressions, matrix decompositions, the coupled Sylvester-like quaternion systems of matrix equations [2][3][4]6,8,14,[20][21][22][23][24]26,27,39,40,[47][48][49][50]52,54,55,57], and the theoretical studies surrounding Sylvester-like quaternion tensor equations. This paper investigates the consistency of and general solution to the following coupled two-sided Sylvester-like quaternion system of tensor equations:…”

Section: Introductionmentioning

confidence: 99%

A new generalization of a system of two-sided coupled Sylvester-like quaternion tensor equations

Wang¹,

Mehany²

2022

Preprint

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This study establishes consistency conditions and a general solution for a coupled system that consists of five two-sided Sylvester-like tensor equations in ten quaternion variables throughout the Einstein tensor product. Certain specific cases are thus established. In a direct application, we investigate certain necessary and sufficient conditions for the existence of an η-Hermitian solution to five coupled two-sided Sylvester-like quaternion tensor equations. Finally, we present an algorithm and a numerical example to validate the main result.

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“…The decompositions of the quaternion matrices have applications in many fields, such as color image processing(e.g., [2,3]), quantum mechanics [4], signal processing [5], and so on. Research on quaternion matrix theories (e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18]) and equations (e.g., [13,[19][20][21][22][23][24][25][26][27]) is ongoing.…”

Section: Introductionmentioning

confidence: 99%

The Solvability of a System of Quaternion Matrix Equations Involving ϕ-Skew-Hermicity

Zhang

Zhao

et al. 2022

Symmetry

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Let H be the real quaternion algebra and Hm×n denote the set of all m×n matrices over H. For A∈Hm×n, we denote by Aϕ the n×m matrix obtained by applying ϕ entrywise to the transposed matrix AT, where ϕ is a non-standard involution of H. A∈Hn×n is said to be ϕ-skew-Hermicity if A=−Aϕ. In this paper, we provide some necessary and sufficient conditions for the existence of a ϕ-skew-Hermitian solution to the system of quaternion matrix equations with four unknowns AiXi(Ai)ϕ+BiXi+1(Bi)ϕ=Ci,(i=1,2,3),A4X4(A4)ϕ=C4.

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A constrained system of matrix equations

Cited by 16 publications

References 26 publications

The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

A new generalization of a system of two-sided coupled Sylvester-like quaternion tensor equations

The Solvability of a System of Quaternion Matrix Equations Involving ϕ-Skew-Hermicity

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