Least squares X=±Xη* solutions to split quaternion matrix equation AXAη*=B
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DOI: 10.1002/mma.6033
Abstract: In the paper, the split quaternion matrix equation AXAη*=B is considered, where the operator Aη* is the η‐conjugate transpose of A, where η∈{i,j,k}. We propose some new real representations, which well exploited the special structures… read more here.
Keywords: least squares; matrix equation; equation; quaternion matrix ... See more keywords
Solvability conditions and general solutions to some quaternion matrix equations
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DOI: 10.1002/mma.7696
Abstract: This paper studies some quaternion matrix equations. We use the equivalence canonical form to present some practical necessary and sufficient conditions for the existence of a solution to the system of quaternion matrix equations in… read more here.
Keywords: quaternion matrix; solvability conditions; matrix equations; conditions general ... See more keywords
Some Properties of the Solution to a System of Quaternion Matrix Equations
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DOI: 10.3390/axioms11120710
Abstract: This paper investigates the properties of the ϕ-skew-Hermitian solution to the system of quaternion matrix equations involving ϕ-skew-Hermicity with four unknowns AiXi(Ai)ϕ+BiXi+1(Bi)ϕ=Ci,(i=1,2,3),A4X4(A4)ϕ=C4. We present the general ϕ-skew-Hermitian solution to this system. Moreover, we derive the… read more here.
Keywords: solution system; system; system quaternion; matrix equations ... See more keywords
An Exact Solution to a Quaternion Matrix Equation with an Application
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DOI: 10.3390/sym14020375
Abstract: In this paper, we establish the solvability conditions and the formula of the general solution to a Sylvester-like quaternion matrix equation. As an application, we give some necessary and sufficient conditions for a system of… read more here.
Keywords: solution; quaternion matrix; matrix equation; equation application ... See more keywords
Solving a System of Sylvester-like Quaternion Matrix Equations
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DOI: 10.3390/sym14051056
Abstract: Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general… read more here.
Keywords: system; quaternion matrix; matrix equations; system sylvester ... See more keywords
An Efficient Method for Split Quaternion Matrix Equation X - Af(X)B = C
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DOI: 10.3390/sym14061158
Abstract: In this paper, we consider the split quaternion matrix equation X−Af(X)B=C, f(X)∈{X,XH,XiH,XjHXkH}. The H representation method has the characteristics of transforming a matrix with a special structure into a column vector with independent elements. By… read more here.
Keywords: quaternion matrix; split quaternion; matrix equation; equation ... See more keywords
The Solvability of a System of Quaternion Matrix Equations Involving ϕ-Skew-Hermicity
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DOI: 10.3390/sym14061273
Abstract: 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… read more here.
Keywords: matrix; system quaternion; matrix equations; skew hermicity ... See more keywords