Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X38120120401Ranks of the common solution to some quaternion matrix equations
with applications131157396ENQ.WangShanghai UniversityS.YuEast China University of Science and TechnologyJournal Article20100810We derive the formulas of the maximal and<br />minimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$<br />in common solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to quaternion<br />matrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. As<br />applications, we establish necessary and sufficient conditions for\<br />the existence of the common real and complex solutions to the matrix<br />equations. We give the expressions of such solutions to this system<br />when the solvability conditions are met. Moreover, we present<br />necessary and sufficient conditions for the existence of real and<br />complex solutions to the system of quaternion<br />matrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3},A_{4}%<br />XB_{4}=C_{4}$. The findings of this paper extend some known results<br />in the literature.http://bims.iranjournals.ir/article_396_b3c2a4e18ed3cb578254fb893db94ade.pdf