Endomorphisms and Diagonalization

Abstract

In this chapter we will study a central topic in the theory of matrices. We have already seen (and I hope we haven’t forgotten) that matrices serve as containers of numerical information, for example as the fundamental parts of linear systems and as an essential mathematical tool for their solution. We’ve multiplied them, we’ve calculated their inverses (when they exist) and we have decomposed them into the LU decomposition. Then we began to appreciate them as geometric tools, in the sense that we have associated them to vectors and systems of coordinates.