ABSTRACT

In this chapter, we start to investigate solution to homogeneous GSEs. The first section introduces an operation that is frequently used in this chapter as well as the other sequential chapters. The following three sections treat the general case of F being an arbitrary matrix and provide complete general parametric expressions for the matricesV andW satisfying the GSE. The primary feature of this solution is that the matrix F does not need to be in any canonical form and may be even unknown a priori. The rest of the sections consider special cases of the matrix F . In Sections 4.5 and 4.6, cases of F being a Jordan matrix and a diagonal matrix are treated, and some examples follow in Section 4.7.