Provide a glimpse of some widely used matrix factorizations, some of which are discussed later in the text.
(Spectral Factorization) Suppose a 3 X 3 matrix A admits a factorization as A = PDP-1, where P is some invertible 3 X 3 matrix and D is the diagonal matrix
![1753_f27d322b-3d2a-4b80-8158-4c6497a697f6.png](https://secure.tutorsglobe.com/CMSImages/1753_f27d322b-3d2a-4b80-8158-4c6497a697f6.png)
Show that this factorization is useful when computing high powers of A. Find fairly simple formulas for A2, A3, and Ak (k a positive integer), using P and the entries in D.