ABSTRACT
In the previous chapter, we saw that a matrix A ∈ Fn×n is diagonalizable if there is a basis of Fn consisting of eigenvectors of A. A matrix failing to satisfy this condition is called defective.
Given that not all matrices can be diagonalized, we wish to determine the simplest form of a matrix that can be obtained by a similarity transformation. Expressed in terms of a linear operator on a finite-dimensional space, the question is how to choose the basis so that the matrix representing the operator is as simple as possible.
