Introduction

In the best of all possible worlds (for some), all matrices would be diagonalizable. Unfortunately, this is not the case. The next best thing is to put a matrix in Jordan canonical form. A theoretical reference for this material is Kenneth Hoffman and Ray Kunze, Linear Algebra. Less theoretical is Gilbert Strang, Linear Algebra and Its Applications. We follow both developmenmts here. Strang's development follows the development of diagonalizing a matrix, so we will review this.

Up to Jordan Canonical Form