Polynomial-Matrix-Based Approaches

In Chap. 6, a kind of real representations for complex matrices has been used to investigate some complex conjugate matrix equations, such as the normal con-Sylvester equations, the con-Yakubovich equations, and the generalized con-Sylvester equations. A basic feature of the approaches in Chap. 6 is that the basic solutions of these matrix equations are obtained by indirectly using the results of their corresponding real representation matrix equations. In this chapter, polynomial matrices are used to investigate some complex conjugate matrix equations. In such a framework, it is not necessary to use relevant results on some matrix equations without the conjugate of the unknown matrices.