Ranks and the least-norm of the general solution to a system of quaternion matrix equations

We in this paper first establish a new expression of the general solution to the consistent system of linear quaternion matrix equations A1X1=C1, A2X2=C2, A3X1B1+A4X2B2=C3, which was investigated recently [Q.W. Wang, H.X. Chang, C.Y. Lin, P-(skew)symmetric common solutions to a pair of quaternion matrix equations, Appl. Math. Comput. 195 (2008) 721–732], then derive the maximal and minimal ranks and the least-norm of the general solution to the system mentioned above. Some previous known results can be viewed as special cases of the results of this paper.