ABSTRACT
The Jordan decomposition is one answer to the following question: Given a finite-dimensional vector space X and a linear operator T : X → X , how can we choose a basis for X so the matrix representing T is as simple as possible? As we saw in the previous chapter, it is not always possible to obtain a diagonal matrix; moreover, the basis that results in the Jordan canonical form cannot always be chosen to be orthonormal. Furthermore, the calculation of the Jordan decomposition is problematic in finite-precision arithmetic.
