TY - JOUR
ID - 396
TI - Ranks of the common solution to some quaternion matrix equations
with applications
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Wang, Q.
AU - Yu, S.
AD - Shanghai University
AD - East China University of Science and Technology
Y1 - 2012
PY - 2012
VL - 38
IS - 1
SP - 131
EP - 157
KW - Quaternion matrix equation
KW - maximal and minimal rank
KW - generalized inverse
KW - real solution
KW - complex solution
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_396.html
L1 - http://bims.iranjournals.ir/article_396_b3c2a4e18ed3cb578254fb893db94ade.pdf
ER -