2013
DOI: 10.1080/03081087.2013.839667
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Abstract: Let H m×n be the set of all m × n matrices over the real quaternion algebra.We in this paper, present the solvability conditions and the general η-Hermitian solution to a system of linear real quaternion matrix equations. As an application, we give the necessary and sufficient conditions for the systemWe establish an expression of the η-bihermitian to the system when it is solvable. We also obtain a criterion for a quaternion matrix to be η-bihermitian. Moreover, we provide an algorithm and a numerical example… Show more

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Cited by 40 publications
(24 citation statements)
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“…The outcome of our exposition extends the noteworthy result of [28,32,33] and [46]. Furthermore, we have given an algorithm and a numerical example to interpret our rudimentary consequence.…”
Section: Resultssupporting
confidence: 52%
See 1 more Smart Citation
“…The outcome of our exposition extends the noteworthy result of [28,32,33] and [46]. Furthermore, we have given an algorithm and a numerical example to interpret our rudimentary consequence.…”
Section: Resultssupporting
confidence: 52%
“…With these conditions, (X, Y, Z) are carried out by At the end, if matrices A 1 , A 4 and C 1 are zero in our system, then we get Theorem 3.1 of [33]. …”
Section: K}) Be Known Matrices In System (13) Denotementioning
confidence: 99%
“…where S A , S B , S C , and S D are given in (9) and (10). Hence the real quaternion matrix equation (31) is equivalent to the real quaternion matrix equation…”
Section: The Solution To (3) With Y Being φ-Hermitianmentioning
confidence: 99%
“…The research on the system of quaternion matrix equations involving η-Hermicity has attracted more and more attentions in recent years (e.g. [8], [9], [23]- [25]). As special cases of the quaternion matrix equations (2) and 3, we can derive some necessary and sufficient conditions for the existence of a solution to the following four quaternion matrix equations involving η-Hermicity for η ∈ {i, j, k}:…”
Section: The Solution To (3) With Y Being φ-Hermitianmentioning
confidence: 99%
“…Some recent work on generalized Sylvester matrix equations and their systems can be observed in [19][20][21][22][23][24][25][26][27][28][29][30][31]. In 2014, Bao [32] examined the least-norm and extremal ranks of the least square solution to the quaternion matrix equations…”
Section: Introductionmentioning
confidence: 99%