A new solvable condition for a pair of generalized Sylvester equations
Qing‐Wen Wang, Huasheng Zhang, Guang‐Jing Song · Electronic Journal of Linear Algebra · 2009
A necessary and sufficient condition is given for the quaternion matrix equationsAiX + Y Bi = Ci (i = 1, 2) to have a pair of common solutions X and Y . As a consequence, theresults partially answer a question posed by Y.H. Liu (Y.H. Liu, Ranks of solutions of the linearmatrix equation AX + Y B = C, Comput. Math. Appl., 52 (2006), pp. 861-872).