ABSTRACT
There is not room in a book like this for a discussion of the mathematical methods that are used for performing mundane chores like actually inverting a matrix or finding its eigenvalues. However, I do wish to treat one problem here because it will come up again in Chapter 11. That is, given a large matrix A, how can we find some of its eigenvalues, if not all of them? Assume that A has the form PtP, so its eigenvalues are non-negative definite. Then there is clearly a largest eigenvalue ?1, and successively smaller ones ?2, ?3, …, with ?i=0. When A is very large, the canned routines for finding eigenvalues may not work, or may work only very slowly. Here is a method that will find the largest eigenvalues.
