Geodesic
The η-Hermitian solutions to some systems of real quaternion matrix equations
Filomat, Tome 36 (2022) no. 1, p. 315

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Let H m×n be the set of all m × n matrices over the real quaternion algebra. We call that A ∈ H n×n is η-Hermitian if A = A η * , where A η * = −ηA * η, η ∈ {i, j, k}, i, j, k are the quaternion units. In this paper, we derive some solvability conditions and the general solution to a system of real quaternion matrix equations. As an application, we present some necessary and sufficient conditions for the existence of an η-Hermitian solution to some systems of real quaternion matrix equations. We also give the expressions of the general η-Hermitian solutions to these systems when they are solvable. Some numerical examples are given to illustrate the results of this paper
DOI : 10.2298/FIL2201315Z
Classification : 15A24, 15A09, 15A03
Keywords: Linear matrix equations, quaternion matrix, general η-Hermitian solution, generalized inverses 
Xiang Zhang. The η-Hermitian solutions to some systems of real quaternion matrix equations. Filomat, Tome 36 (2022) no. 1, p. 315 . doi: 10.2298/FIL2201315Z
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     author = {Xiang Zhang},
     title = {The {\ensuremath{\eta}-Hermitian} solutions to some systems of real quaternion matrix equations},
     journal = {Filomat},
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     year = {2022},
     volume = {36},
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     doi = {10.2298/FIL2201315Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2201315Z/}
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