The Jordan Canonical Form

The main result in this chapter allows us to write a square matrix A as A = SJS−1, where J is a particularly simple matrix (in some cases a diagonal matrix). In light of the results in Section 3.3, this means that for a linear transformation on a finite-dimensional vector space we can find a simple matrix representation J (called the Jordan canonical form). This is helpful when one wants to work with this linear transformation. For example, we will see how the Jordan canonical form is helpful in solving a system of linear differential equations.