Spectra and Examples

In this chapter we introduce the notions of tempered exponential dichotomy and of tempered spectrum for a sequence of \(d \times d\) matrices that need not be invertible. The tempered spectrum can be thought of as a nonautonomous version of the usual notion of spectrum for a single matrix. We also describe all possible forms of the tempered spectrum and we give explicit examples of all of them. More precisely, for each possible form we describe explicitly a sequence of invertible matrices with that tempered spectrum.