The η-anti-Hermitian solution to some classic matrix equations

We in this paper consider the η-anti-Hermitian solution to some classic matrix equations AX=B,AXB=C,AXAη*=B,EXEη*+FYFη*=H, respectively. We derive the necessary and sufficient conditions for the above matrix equations to have η-anti-Hermitian solutions and also provide the general expressions of solutions when those equations are solvable. As applications, for instance, we give the solvability conditions and general η-anti-Hermitian solution to equation system AX=B,CY=D,MXMη*+NYNη*=G.