Least-norm and Extremal Ranks of the Least Square Solution to the Quaternion Matrix Equation AXB=C Subject to Two Equations

In this paper, we give the expression of the least square solution of the linear quaternion matrix equation AXB=C subject to a consistent system of quaternion matrix equations D₁X=F₁, XE₂=F₂, and derive the maximal and minimal ranks and the least-norm of the above mentioned solution. The finding of this paper extends some known results in the literature.