Ranks of a Partitioned Quaternion Matrix under a Pair of Matrix Equations

摘要

We establish a theorem for the maximal and minimal ranks of a 2 x 2 par-titioned quaternion matrix whose submatrix X at the right top corner is a commonsolution to a joint quaternion matrix equations A_1 X =XB_1 =C_2.A known resultin this topic can be regarded as a special case of our theorem.