Abstract
This paper studies a system of three Sylvester-type quaternion matrix equations with ten variables \({A_i}{X_i} + {Y_i}{B_i} + {C_i}{Z_i}{D_i} + {F_i}{Z_{i + 1}}{G_i} = {E_i},\,\,\,i = \overline {1,3} \). We derive some necessary and sufficient conditions for the existence of a solution to this system in terms of ranks and Moore-Penrose inverses of the matrices involved. We present the general solution to the system when the solvability conditions are satisfied. As applications of this system, we provide some solvability conditions and general solutions to some systems of quaternion matrix equations involving ϕ-Hermicity. Moreover, we give some numerical examples to illustrate our results. The findings of this paper extend some known results in the literature.
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Supported by the National Natural Science Foundation of China (Grant No. 11971294)
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**e, M.Y., Wang, Q.W., He, Z.H. et al. A System of Sylvester-type Quaternion Matrix Equations with Ten Variables. Acta. Math. Sin.-English Ser. 38, 1399–1420 (2022). https://doi.org/10.1007/s10114-022-9040-1
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DOI: https://doi.org/10.1007/s10114-022-9040-1