Spectral Theory

In this chapter, it is assumed that all linear spaces under consideration are over the real field ℝ and that all linear and inner-product spaces are finite-dimensional. However, in Sects.89 and 810 we deal with linear spaces over ℝ that are at the same time linear spaces over the complex field ℂ. Most of this chapter actually deals with a given finite-dimensional genuine inner-product space. Some of the definitions remain meaningful and some of the results remain valid if the space is infinite-dimensional or if ℝ is replaced by an arbitrary field.