%0 Journal Article
%T Ranks of the common solution to some quaternion matrix equations
with applications
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Wang, Q.
%A Yu, S.
%D 2012
%\ 04/01/2012
%V 38
%N 1
%P 131-157
%! Ranks of the common solution to some quaternion matrix equations
with applications
%K Quaternion matrix equation
%K maximal and minimal rank
%K generalized inverse
%K real solution
%K complex solution
%R
%X We derive the formulas of the maximal andminimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$in common solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to quaternionmatrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. Asapplications, we establish necessary and sufficient conditions for\the existence of the common real and complex solutions to the matrixequations. We give the expressions of such solutions to this systemwhen the solvability conditions are met. Moreover, we presentnecessary and sufficient conditions for the existence of real andcomplex solutions to the system of quaternionmatrix 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 resultsin the literature.
%U http://bims.iranjournals.ir/article_396_b3c2a4e18ed3cb578254fb893db94ade.pdf