2East China University of Science and Technology, Shanghai 200237, P.R. China
Abstract
We in this paper derive the formulas of the maximal and
minimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$
in solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to the common solution of
quaternion matrix equations
$A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. As applications, we
establish necessary and sufficient conditions for the existence of
the common real and complex solutions to the matrix equations. We
give the expressions of such solutions to this system when the
solvability conditions are met. Moreover, we present necessary and
sufficient conditions for the existence of real and complex
solutions to the system of quaternion
matrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3},A_{4}%
XB_{4}=C_{4}$. The findings of this paper extend some known results
in the literature.
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