Mathematical Tools

Abstract

In this chapter we review some definitions and results, mainly from multilinear algebra and differential geometry, which we shall need. The reader who is well-versed in differential geometry need only skim it to absorb the notation, while one whose knowledge stems from a half-remembered course taken years ago will probably need to read it more carefully. Few proofs are given, but most of the omitted arguments are trivial or routine; those which are not are clearly flagged. The ability to fill the gaps, or at least sense how the proofs might go, could be taken as a test as to whether the reader has the background for Chapters 3 and 4.