‎Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices

Abstract

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexive and anti-reflexive matrices‎. ‎The convergence of the iterative methods is also proposed‎. ‎Finally‎, ‎a numerical example is given to show the efficiency of the presented results‎.