The reflexive and anti-reflexive unitary solutions to matrix equationsAX=BandXC=D

For a given generalized reflection matrix P, the reflexive and anti-reflexive unitary solutions to matrix equations AX= Band XC= Dwith respect to generalized reflection matrix Pare investigated. By using singular value decomposition and spectral decomposition of symmetric matrix, the explicit expressions for the constraint solutions mentioned above are obtained. Finally, numerical examples are presented to illustrate and explain our results.