Ranks of submatrices in (skew-)Hermitian solutions to a quaternion matrix equation
Assume that X and Y are Hermitian solutions to quaternion matrix equation AXA ?+BYB ?=C, which are partitioned into 22 block forms. We in this paper give the maximal and minimal ranks of submatrices in the Hermitian solutions X=X ?, Y=Y ?, and establish necessary and sufficient conditions for the submatrices to be zero, unique as well as independent. The findings of this paper widely extend the known results in the literature.
hermitian solution quaternion matrix equation minimal rank maximal rank skew-hermitian solution hermitian generalized inverse 15a03 15a09 15a24 15a33