TY - JOUR ID - 364 TI - The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2 JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Dehghan, M. AU - Hajarian, M. AD - Y1 - 2011 PY - 2011 VL - 37 IS - No. 3 SP - 269 EP - 279 KW - Matrix equation KW - (R KW - S)-symmetric matrix KW - S)-skew symmetric matrix DO - N2 - Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in engineering and scientific computating. Here, we introduce the necessary and sufficient conditions for the solvability of the pair of matrix equations $A_{1}XB_{1}=C_{1}$ and $A_{2}XB_{2}=C_{2}$, over $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices, and give the general expressions of the solutions for the solvable cases. Finally, we give necessary and sufficient conditions for the existence of $(R, S)$-symmetric and $(R, S)$-skew symmetric solutions and representations of these solutions to the pair of matrix equations in some special cases. UR - http://bims.iranjournals.ir/article_364.html L1 - http://bims.iranjournals.ir/article_364_7532efcddc42e213d1eae59596ad5a4a.pdf ER -