Matrix equations over (R,S) ( R , S ) -symmetric and (R,S) ( R , S ) -skew symmetric matrices
Let R?Cmm R ? C m  m and S?Cnn S ? C n  n be nontrivial involution matrices; i.e.R=R?1?I R = R ? 1 ?  I and S=S?1?I S = S ? 1 ?  I . An mn m  n complex matrix A A is said to be a (R,S) ( R , S ) -symmetric ((R,S) ( R , S ) -skew symmetric) matrix if RAS=A R A S = A (RAS=?A R A S = ? A ). The (R,S) ( R , S ) -symmetric and (R,S) ( R , S ) -skew symmetric matrices have many special properties and are widely used in engineering and scientific computations. In this paper, we consider the matrix equations
matrix equation (r (r s) ( r s) ( r s) ( r s) ( r s) ( r s ) s) ( r s) ( r s) ( r s) ( r s) ( r s ) s ) -symmetric (r s ) (r s ) ( r s ) -skew symmetric (r generalized inverse reflexive inverse