Uses of cayley-hamilton theorem and diagonalizability revisited

Uses of cayley-hamilton theorem and diagonalizability revisited Uses of Cayley-Hamilton Theorem: Expressing higher power of a matrix as a linear combinations of the lower powers of that matrix Finding inverse of non-singular matrices using Cayley-Hamilton theorem Diagonalizability Revisited How to find an arbitraily close diagonalizable matrix to a given matrix Theorems relatied to similar matrices given any arbitray matrix