Ranks of Submatrices in a Solution to a Consistent System of Linear Quaternion Matrix Equations with Applications

Suppose that A(1)X = C-1, X B-2 = C-2 A(3) X B-3 = C-3 is a consistent system of matrix equations and partition its solution X into a 2 x 2 block form. In this paper, we give formulas for the maximal and minimal ranks of the submatrices in a solution X to the system. We also investigate the uniqueness and the independence of submatrices in a solution X. As applications, we give some properties of submatrices in generalized inverses of matrices. These extend some known results in the literature.